7-4 Trigonometric Ratios

11-7 Trigonometric Ratios

Trigonometry is the study of triangles.

In right triangles, The sides and angles are all related

Right Triangle Review

HYPOTENUSE

VOCAB TO KNOW adjacent : “next to”, but not the hypotenuse. opposite: “across from” What measure is adjacent to a°? What measure is opposite to a°?

5 3 a° 4

Memorize This: SOH

CAH

TO-A

SOH - CAH - TO - A

SOH

CAH TOA !!

SOH CAH

TOA

SIN The sine of an angle is a ratio: opposite / hypotenuse.

What is sin(g) ?

g°

5

3

4 sin(g)= 5

k° 4

What about the sin(k) ?

g°

3 sin(k) = 5

5

3

k° 4

COS The cosine of an angle is the ratio: adjacent / hypotenuse

3 cos(g) = 5

g°

4 cos(k) = 5

5

3

k° 4

TAN The tangent of an angle is the ratio: opposite / adjacent 4

tan(g) =

g°

tan(k) =

5

3

k° 4

3 3 4

Sine = Opposite / Hypotenuse

SOH

Cosine = Adjacent / Hypotenuse Tangent = Opposite / Adjacent

CAH TOA

• On your calculator, hit

MODE

and third one down, make sure it is in “Degree” mode. If not, move over it and hit ENTER.

We can use these to find missing measurements of a right triangle.

Set up an equation.

45°

15

a sin(45°) = 15 a .7071 ≈ 15 a ≈ 10.6

a

Find the degree measure

Set up an equation:

x°

13 sin-1 sin(x) = sin 18 -1 x To = sin (13/18) undo the sin, 18

13

-1

multiply both sides by sin-1 Use the calcalatah!