Unit Circle Flashcards
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Copyright Agreement These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted below are reserved. You are encouraged to reproduce these materials in whole or in part for use within your educational institution provided appropriate credit is given. You may distribute these materials to other institutions or representatives thereof only if the entire work is transferred in its complete, unaltered form, either as an original Microsoft Word file or as an original, high quality printout. If you a have questions about this agreement please contact the author (e-mail [email protected]).
Unit Circle Trigonometric Flash Cards Target Audience: Algebra II, Trigonometry, Pre-Calculus Play in groups of two to four students.
Unit Circle Trigonometric Flash Cards 1) Deal cards evenly among students. 2) Students take turns showing/asking the questions Q to the other students in the group. Whoever answers the question correctly wins the card. 3) Hints are available on each answer card if necessary. The student asking may guide the others by asking questions such as A) What quadrant is it in? B) Is it a horizontal (cosine) or vertical (sine)? C) Is it positive or negative? 4) The player with the most cards wins the round. 5) Repeat as many times as necessary. Alternative Game is to play like JEOPARDY Students would show/ask the answers A including the hints. Others would respond with appropriate trig function and angle in both degrees and radians. TEACHER NOTE: To make card sets, photocopy the following pages as a collated set of cards. These cards must be photocopied as double-sided with question cards (marked with Q) on one side and answer cards (marked with A) on the other. For a class of 28 make 7 collated sets. Indicate the cards that belong to the same set using different colored paper for each set. If one card is found in a desk or on the floor you will be able to match it to the correct set easily. Laminate each page. Get 7 zip-lock bags, one for each card set. Use a paper cutter to cut the cards for one set and seal in the zip-lock bag as you cut. Sets can be easily stored in a plastic bin or larger zip-lock bag. These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
cos ( 0 ) = cos ( 0D ) =
⎛π ⎞ cos ⎜ ⎟ = cos ( 30D ) = ? ⎝6⎠
cos ( 2π ) = cos ( 360D ) = ? Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
Q
Q
sin ( 0 ) = sin ( 0D ) =
⎛π ⎞ sin ⎜ ⎟ = sin ( 30D ) = ? ⎝6⎠
sin ( 2π ) = sin ( 360D ) = ? Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
Q
Q
tan ( 0 ) = tan ( 0D ) =
⎛π ⎞ tan ⎜ ⎟ = tan ( 30D ) = ? ⎝6⎠
tan ( 2π ) = tan ( 360D ) = ? Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A QI: long horizontal
A
3 2
1
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
A QI: short vertical
A
1 2
QI:
short vertical long horizontal
positive X-axis
0
Unit CircleTrigonometric Flash Cards
A
positive X-axis
Unit CircleTrigonometric Flash Cards
A
positive X-axis
1 2 = 1 = 3 3 3 3 2
0 =0 1
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
⎛π ⎞ cos ⎜ ⎟ = cos ( 45D ) = ? ⎝4⎠
⎛π ⎞ cos ⎜ ⎟ = cos ( 60D ) = ? ⎝3⎠
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
Q
Q
⎛π ⎞ sin ⎜ ⎟ = sin ( 45D ) = ? ⎝4⎠
⎛π ⎞ sin ⎜ ⎟ = sin ( 60D ) = ? ⎝3⎠
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
Q
Q
⎛π ⎞ tan ⎜ ⎟ = tan ( 45D ) = ? ⎝4⎠
⎛π ⎞ tan ⎜ ⎟ = tan ( 60D ) = ? ⎝3⎠
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A
A
A
QI: short horizontal
A QI: equal length horizontal
1 2
2 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
QI: long vertical
A QI: equal length vertical
3 2
2 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
QI:
long vertical short horizontal
3 2 = 3= 3 1 1 2 Unit CircleTrigonometric Flash Cards
A
QI:
equal length vertical equal length horizontal
2 2 =1 2 2 Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
⎛π ⎞ cos ⎜ ⎟ = cos ( 90D ) = ? ⎝2⎠
⎛ 2π cos ⎜ ⎝ 3
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
Q
Q
⎛π ⎞ sin ⎜ ⎟ = sin ( 90D ) = ? ⎝2⎠
⎛ 2π sin ⎜ ⎝ 3
Unit CircleTrigonometric Flash Cards
⎞ D = =? sin 120 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
Q
⎛π ⎞ tan ⎜ ⎟ = tan ( 90D ) = ? ⎝2⎠
⎛ 2π tan ⎜ ⎝ 3
Unit CircleTrigonometric Flash Cards
⎞ D cos 120 = =? ( ) ⎟ ⎠
⎞ D = =? tan 120 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A QII: short horizontal
A
1 − 2
0
Unit CircleTrigonometric Flash Cards
A
QII: long vertical
positive Y-axis
Unit CircleTrigonometric Flash Cards
A
positive Y-axis
3 2
1
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
A QII:
long vertical short horizontal
A
positive Y-axis
3 2 = 3 =− 3 −1 −1 2
1 =undefined 0
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
⎛ 3π cos ⎜ ⎝ 4
⎞ D = =? cos 135 ( ) ⎟ ⎠
⎛ 5π cos ⎜ ⎝ 6
Unit CircleTrigonometric Flash Cards
Q
⎞ D cos 150 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 3π sin ⎜ ⎝ 4
⎞ D = =? sin 135 ( ) ⎟ ⎠
⎛ 5π sin ⎜ ⎝ 6
Unit CircleTrigonometric Flash Cards
Q
⎞ D sin 150 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 3π tan ⎜ ⎝ 4
⎞ D = =? tan 135 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
⎛ 5π tan ⎜ ⎝ 6
⎞ D tan 150 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A
QII: long horizontal
A QII: equal length horizontal
3 − 2
2 − 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
A QII: short vertical
A QII: equal length vertical
1 2
2 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
A
QII:
short vertical long horizontal
1 2
1 3 =− =− 3 3 − 3 2 Unit CircleTrigonometric Flash Cards
A
QII:
equal length vertical equal length horizontal
2 2 = −1 − 2 2 Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
⎛ 7π cos ⎜ ⎝ 4
⎞ D = =? cos 315 ( ) ⎟ ⎠
⎛ 5π cos ⎜ ⎝ 4
Unit CircleTrigonometric Flash Cards
Q
⎞ D = =? cos 225 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 7π sin ⎜ ⎝ 4
⎞ D = =? sin 315 ( ) ⎟ ⎠
⎛ 5π sin ⎜ ⎝ 4
Unit CircleTrigonometric Flash Cards
Q
⎞ D sin 225 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 7π tan ⎜ ⎝ 4
⎞ D = =? tan 315 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
⎛ 5π tan ⎜ ⎝ 4
⎞ D tan 225 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A
QIII: equal length horizontal
A
QIV: equal length horizontal
2 2
2 − 2 Unit CircleTrigonometric Flash Cards
A
A
QIII: equal length vertical
Unit CircleTrigonometric Flash Cards
A
QIV: equal length vertical
2 − 2
2 − 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
QIII:
equal length vertical equal length horizontal
A
QIV:
equal length vertical equal length horizontal
− 2 2 =1 − 2 2
− 2 2 = −1 2 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
⎛ 4π cos ⎜ ⎝ 3
⎞ D cos 240 = =? ( ) ⎟ ⎠
⎛ 5π cos ⎜ ⎝ 3
Unit CircleTrigonometric Flash Cards
Q
⎞ D cos 300 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 4π sin ⎜ ⎝ 3
⎞ D = =? sin 240 ( ) ⎟ ⎠
⎛ 5π sin ⎜ ⎝ 3
Unit CircleTrigonometric Flash Cards
Q
⎞ D = =? sin 300 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 4π tan ⎜ ⎝ 3
⎞ D = =? tan 240 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
⎛ 5π tan ⎜ ⎝ 3
⎞ D = =? tan 300 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A QIV: short horizontal
1 2
1 − 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
A QIV: long vertical
A
A QIII: short horizontal
A
QIII: long vertical
3 − 2
3 − 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
QIV:
long vertical short horizontal
A
QIII:
long vertical short horizontal
− 3 2 =− 3 =− 3 1 1 2
− 3 2 = 3= 3 1 1 − 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
⎛ 11π cos ⎜ ⎝ 6
⎞ D = =? cos 330 ( ) ⎟ ⎠
⎛ 7π cos ⎜ ⎝ 6
Unit CircleTrigonometric Flash Cards
Q
⎞ D cos 210 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 11π sin ⎜ ⎝ 6
⎞ D sin 330 = =? ( ) ⎟ ⎠
⎛ 7π sin ⎜ ⎝ 6
Unit CircleTrigonometric Flash Cards
Q
⎞ D sin 210 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 11π tan ⎜ ⎝ 6
⎞ D tan 330 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
⎛ 7π tan ⎜ ⎝ 6
⎞ D = =? tan 210 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A QIII: long horizontal
A
A
A QIV: long horizontal
3 − 2
3 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
QIII: short vertical
A
QIV: short vertical
1 − 2
1 − 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
QIII:
short vertical long horizontal
A
QIV:
short vertical long horizontal
−1 2 = −1 = 3 3 − 3 − 3 2
−1 2 = −1 = − 3 3 3 3 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
⎛ 3π cos ⎜ ⎝ 2
⎞ D cos 270 = =? ( ) ⎟ ⎠
cos (π ) = cos (180D ) = ?
Unit CircleTrigonometric Flash Cards
Q
Unit CircleTrigonometric Flash Cards
Q
⎛ 3π sin ⎜ ⎝ 2
⎞ D sin 270 = =? ( ) ⎟ ⎠
sin (π ) = sin (180D ) = ?
Unit CircleTrigonometric Flash Cards
Q
Unit CircleTrigonometric Flash Cards
Q
⎛ 3π tan ⎜ ⎝ 2
⎞ D = =? tan 270 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
tan (π ) = tan (180D ) = ?
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A
negative X-axis
A
−1
0
Unit CircleTrigonometric Flash Cards
A
A
negative X-axis
negative Y-axis
Unit CircleTrigonometric Flash Cards
A
negative Y-axis
0
−1
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
negative X-axis
0 =0 1 Unit CircleTrigonometric Flash Cards
A
negative Y-axis
−1 =undefined 0 Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Unit Circle Trigonometric Flash Cards Target Audience: Algebra II, Trigonometry, Pre-Calculus Play in groups of two to four students.
Unit Circle Trigonometric Flash Cards 1) Deal cards evenly among students. 2) Students take turns showing/asking the questions Q to the other students in the group. Whoever answers the question correctly wins the card. 3) Hints are available on each answer card if necessary. The student asking may guide the others by asking questions such as A) What quadrant is it in? B) Is it a horizontal (cosine) or vertical (sine)? C) Is it positive or negative? 4) The player with the most cards wins the round. 5) Repeat as many times as necessary. Alternative Game is to play like JEOPARDY Students would show/ask the answers A including the hints. Others would respond with appropriate trig function and angle in both degrees and radians. TEACHER NOTE: To make card sets, photocopy the following pages as a collated set of cards. These cards must be photocopied as double-sided with question cards (marked with Q) on one side and answer cards (marked with A) on the other. For a class of 28 make 7 collated sets. Indicate the cards that belong to the same set using different colored paper for each set. If one card is found in a desk or on the floor you will be able to match it to the correct set easily. Laminate each page. Get 7 zip-lock bags, one for each card set. Use a paper cutter to cut the cards for one set and seal in the zip-lock bag as you cut. Sets can be easily stored in a plastic bin or larger zip-lock bag. These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
cos ( 0 ) = cos ( 0D ) =
⎛π ⎞ cos ⎜ ⎟ = cos ( 30D ) = ? ⎝6⎠
cos ( 2π ) = cos ( 360D ) = ? Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
Q
Q
sin ( 0 ) = sin ( 0D ) =
⎛π ⎞ sin ⎜ ⎟ = sin ( 30D ) = ? ⎝6⎠
sin ( 2π ) = sin ( 360D ) = ? Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
Q
Q
tan ( 0 ) = tan ( 0D ) =
⎛π ⎞ tan ⎜ ⎟ = tan ( 30D ) = ? ⎝6⎠
tan ( 2π ) = tan ( 360D ) = ? Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A QI: long horizontal
A
3 2
1
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
A QI: short vertical
A
1 2
QI:
short vertical long horizontal
positive X-axis
0
Unit CircleTrigonometric Flash Cards
A
positive X-axis
Unit CircleTrigonometric Flash Cards
A
positive X-axis
1 2 = 1 = 3 3 3 3 2
0 =0 1
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
⎛π ⎞ cos ⎜ ⎟ = cos ( 45D ) = ? ⎝4⎠
⎛π ⎞ cos ⎜ ⎟ = cos ( 60D ) = ? ⎝3⎠
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
Q
Q
⎛π ⎞ sin ⎜ ⎟ = sin ( 45D ) = ? ⎝4⎠
⎛π ⎞ sin ⎜ ⎟ = sin ( 60D ) = ? ⎝3⎠
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
Q
Q
⎛π ⎞ tan ⎜ ⎟ = tan ( 45D ) = ? ⎝4⎠
⎛π ⎞ tan ⎜ ⎟ = tan ( 60D ) = ? ⎝3⎠
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A
A
A
QI: short horizontal
A QI: equal length horizontal
1 2
2 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
QI: long vertical
A QI: equal length vertical
3 2
2 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
QI:
long vertical short horizontal
3 2 = 3= 3 1 1 2 Unit CircleTrigonometric Flash Cards
A
QI:
equal length vertical equal length horizontal
2 2 =1 2 2 Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
⎛π ⎞ cos ⎜ ⎟ = cos ( 90D ) = ? ⎝2⎠
⎛ 2π cos ⎜ ⎝ 3
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
Q
Q
⎛π ⎞ sin ⎜ ⎟ = sin ( 90D ) = ? ⎝2⎠
⎛ 2π sin ⎜ ⎝ 3
Unit CircleTrigonometric Flash Cards
⎞ D = =? sin 120 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
Q
⎛π ⎞ tan ⎜ ⎟ = tan ( 90D ) = ? ⎝2⎠
⎛ 2π tan ⎜ ⎝ 3
Unit CircleTrigonometric Flash Cards
⎞ D cos 120 = =? ( ) ⎟ ⎠
⎞ D = =? tan 120 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A QII: short horizontal
A
1 − 2
0
Unit CircleTrigonometric Flash Cards
A
QII: long vertical
positive Y-axis
Unit CircleTrigonometric Flash Cards
A
positive Y-axis
3 2
1
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
A QII:
long vertical short horizontal
A
positive Y-axis
3 2 = 3 =− 3 −1 −1 2
1 =undefined 0
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
⎛ 3π cos ⎜ ⎝ 4
⎞ D = =? cos 135 ( ) ⎟ ⎠
⎛ 5π cos ⎜ ⎝ 6
Unit CircleTrigonometric Flash Cards
Q
⎞ D cos 150 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 3π sin ⎜ ⎝ 4
⎞ D = =? sin 135 ( ) ⎟ ⎠
⎛ 5π sin ⎜ ⎝ 6
Unit CircleTrigonometric Flash Cards
Q
⎞ D sin 150 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 3π tan ⎜ ⎝ 4
⎞ D = =? tan 135 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
⎛ 5π tan ⎜ ⎝ 6
⎞ D tan 150 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A
QII: long horizontal
A QII: equal length horizontal
3 − 2
2 − 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
A QII: short vertical
A QII: equal length vertical
1 2
2 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
A
QII:
short vertical long horizontal
1 2
1 3 =− =− 3 3 − 3 2 Unit CircleTrigonometric Flash Cards
A
QII:
equal length vertical equal length horizontal
2 2 = −1 − 2 2 Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
⎛ 7π cos ⎜ ⎝ 4
⎞ D = =? cos 315 ( ) ⎟ ⎠
⎛ 5π cos ⎜ ⎝ 4
Unit CircleTrigonometric Flash Cards
Q
⎞ D = =? cos 225 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 7π sin ⎜ ⎝ 4
⎞ D = =? sin 315 ( ) ⎟ ⎠
⎛ 5π sin ⎜ ⎝ 4
Unit CircleTrigonometric Flash Cards
Q
⎞ D sin 225 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 7π tan ⎜ ⎝ 4
⎞ D = =? tan 315 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
⎛ 5π tan ⎜ ⎝ 4
⎞ D tan 225 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A
QIII: equal length horizontal
A
QIV: equal length horizontal
2 2
2 − 2 Unit CircleTrigonometric Flash Cards
A
A
QIII: equal length vertical
Unit CircleTrigonometric Flash Cards
A
QIV: equal length vertical
2 − 2
2 − 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
QIII:
equal length vertical equal length horizontal
A
QIV:
equal length vertical equal length horizontal
− 2 2 =1 − 2 2
− 2 2 = −1 2 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
⎛ 4π cos ⎜ ⎝ 3
⎞ D cos 240 = =? ( ) ⎟ ⎠
⎛ 5π cos ⎜ ⎝ 3
Unit CircleTrigonometric Flash Cards
Q
⎞ D cos 300 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 4π sin ⎜ ⎝ 3
⎞ D = =? sin 240 ( ) ⎟ ⎠
⎛ 5π sin ⎜ ⎝ 3
Unit CircleTrigonometric Flash Cards
Q
⎞ D = =? sin 300 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 4π tan ⎜ ⎝ 3
⎞ D = =? tan 240 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
⎛ 5π tan ⎜ ⎝ 3
⎞ D = =? tan 300 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A QIV: short horizontal
1 2
1 − 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
A QIV: long vertical
A
A QIII: short horizontal
A
QIII: long vertical
3 − 2
3 − 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
QIV:
long vertical short horizontal
A
QIII:
long vertical short horizontal
− 3 2 =− 3 =− 3 1 1 2
− 3 2 = 3= 3 1 1 − 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
⎛ 11π cos ⎜ ⎝ 6
⎞ D = =? cos 330 ( ) ⎟ ⎠
⎛ 7π cos ⎜ ⎝ 6
Unit CircleTrigonometric Flash Cards
Q
⎞ D cos 210 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 11π sin ⎜ ⎝ 6
⎞ D sin 330 = =? ( ) ⎟ ⎠
⎛ 7π sin ⎜ ⎝ 6
Unit CircleTrigonometric Flash Cards
Q
⎞ D sin 210 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
Q
⎛ 11π tan ⎜ ⎝ 6
⎞ D tan 330 = =? ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
⎛ 7π tan ⎜ ⎝ 6
⎞ D = =? tan 210 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A QIII: long horizontal
A
A
A QIV: long horizontal
3 − 2
3 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
QIII: short vertical
A
QIV: short vertical
1 − 2
1 − 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
QIII:
short vertical long horizontal
A
QIV:
short vertical long horizontal
−1 2 = −1 = 3 3 − 3 − 3 2
−1 2 = −1 = − 3 3 3 3 2
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
Q
Q
⎛ 3π cos ⎜ ⎝ 2
⎞ D cos 270 = =? ( ) ⎟ ⎠
cos (π ) = cos (180D ) = ?
Unit CircleTrigonometric Flash Cards
Q
Unit CircleTrigonometric Flash Cards
Q
⎛ 3π sin ⎜ ⎝ 2
⎞ D sin 270 = =? ( ) ⎟ ⎠
sin (π ) = sin (180D ) = ?
Unit CircleTrigonometric Flash Cards
Q
Unit CircleTrigonometric Flash Cards
Q
⎛ 3π tan ⎜ ⎝ 2
⎞ D = =? tan 270 ( ) ⎟ ⎠
Unit CircleTrigonometric Flash Cards
tan (π ) = tan (180D ) = ?
Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
A
negative X-axis
A
−1
0
Unit CircleTrigonometric Flash Cards
A
A
negative X-axis
negative Y-axis
Unit CircleTrigonometric Flash Cards
A
negative Y-axis
0
−1
Unit CircleTrigonometric Flash Cards
Unit CircleTrigonometric Flash Cards
negative X-axis
0 =0 1 Unit CircleTrigonometric Flash Cards
A
negative Y-axis
−1 =undefined 0 Unit CircleTrigonometric Flash Cards
These materials are copyright © 2003 by the author Catherine A. Eagen. All rights not explicitly granted are reserved.
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