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GOVT. SENIOR SECONDARY SCHOOL TALWARA-1 (HOSHIARPUR) Project:- Trigonometry Prepared by:
Introduction:-
Nardev Singh (Maths Master) Kulwant Singh (Maths Master)
Trigonometry is an important branch of
mathematics. The word trigonometry is derived from a combination of three Greek words ‘tri’, ‘gon’, ‘metron’.’Tri’ means three, ‘gon’ means sides and ‘metron’ means a measure. Thus trigonometry deals with the measurement of the sides of a triangle.
Trigonometric Ratios of angles:Let us take any acute angle AOB. Let us take a point on ray OB and drop the perpendicular PQ on OA. Let us denote the angle POQ by the Greek Letter θ (theta). Then we have a right triangle POQ in which ∟QOP= θ.
In the triangle POQ, OQ is the side adjacent to angle θ (base) and PQ is the side opposite to angle θ (perpendicular). Op is the hypotenuse of the triangle. Here θ is measured in degrees.
Using the lengths of the sides of the right triangle POQ, we define the trigonometric ratios of angle θ as follows: 1.
Sine θ
2.
Cosine θ
3.
Tangent θ
=
Side opposite to angle θ Hypotenuse
=
=
=
PQ OP
Side adjacent to angle θ Hypotenuse
=
OQ OP
Side opposite to angle θ Side adjacent to angle θ
=
PQ OQ
4.
Cosec θ
=
Hypotenuse Side opposite to angle θ
=
OP = 1 PQ sine θ
5.
Sec θ
=
Hypotenuse Side adjacent to angle θ
=
OP = 1 OQ cos θ
6.
Cot θ
=
Side adjacent to angle θ Side opposite to angle θ
=
OQ = 1 PQ tan θ
Values of Trigonometric ratios of 00, 300, 450, 600, 900 θ
sine θ
cos θ
tan θ
cosec θ
sec θ
cot θ
00
0
1
0
1
300
½
√3/2
1/√3
Not defined 2
2/√3
Not defined √3
450
1/√2
1/√2
1
√2
√2
1
600
√3/2
½
√3
2/√3
2
1/√3
900
1
0
Not defined
1
Not defined
0
Acknowledgement:We are very thankful to Mr. Gulshan Rai (Computer Faculty), Mr. Narinder Singh (Computer Faculty) and Miss Amita (Computer Teacher) for their expert guidance and kind co-operation.
Bibliography:1. Computer Teachers 2. Text Books
Introduction:-
Nardev Singh (Maths Master) Kulwant Singh (Maths Master)
Trigonometry is an important branch of
mathematics. The word trigonometry is derived from a combination of three Greek words ‘tri’, ‘gon’, ‘metron’.’Tri’ means three, ‘gon’ means sides and ‘metron’ means a measure. Thus trigonometry deals with the measurement of the sides of a triangle.
Trigonometric Ratios of angles:Let us take any acute angle AOB. Let us take a point on ray OB and drop the perpendicular PQ on OA. Let us denote the angle POQ by the Greek Letter θ (theta). Then we have a right triangle POQ in which ∟QOP= θ.
In the triangle POQ, OQ is the side adjacent to angle θ (base) and PQ is the side opposite to angle θ (perpendicular). Op is the hypotenuse of the triangle. Here θ is measured in degrees.
Using the lengths of the sides of the right triangle POQ, we define the trigonometric ratios of angle θ as follows: 1.
Sine θ
2.
Cosine θ
3.
Tangent θ
=
Side opposite to angle θ Hypotenuse
=
=
=
PQ OP
Side adjacent to angle θ Hypotenuse
=
OQ OP
Side opposite to angle θ Side adjacent to angle θ
=
PQ OQ
4.
Cosec θ
=
Hypotenuse Side opposite to angle θ
=
OP = 1 PQ sine θ
5.
Sec θ
=
Hypotenuse Side adjacent to angle θ
=
OP = 1 OQ cos θ
6.
Cot θ
=
Side adjacent to angle θ Side opposite to angle θ
=
OQ = 1 PQ tan θ
Values of Trigonometric ratios of 00, 300, 450, 600, 900 θ
sine θ
cos θ
tan θ
cosec θ
sec θ
cot θ
00
0
1
0
1
300
½
√3/2
1/√3
Not defined 2
2/√3
Not defined √3
450
1/√2
1/√2
1
√2
√2
1
600
√3/2
½
√3
2/√3
2
1/√3
900
1
0
Not defined
1
Not defined
0
Acknowledgement:We are very thankful to Mr. Gulshan Rai (Computer Faculty), Mr. Narinder Singh (Computer Faculty) and Miss Amita (Computer Teacher) for their expert guidance and kind co-operation.
Bibliography:1. Computer Teachers 2. Text Books
