9.6 Sine and Cosine

CHIEF SOH-CAH-TOA

SOH CAH TOA

H

Osin

H

Acos

A

Otan

Geogebra Investigation

1) Open up the tangent.ggb file on scevmath.org.

2) Use the length tool to find the lengths of the hypotenuse’s, opposite legs and adjacent legs of each of the right triangles.

3) Find the sin 30 and cos 30.

Find the length of x

13

x

40

Find the length of x

16

x

50

Guided PracticeDraw a 30-60-90 and 45-45-90 triangle. 1) Find:

sin 30, sin 45, sin 60, cos 30, cos 45, cos 60

2) What is the relationship between:sin 30 and cos 60sin 45 and cos 45sin 60 and cos 3030 and 60 degree angles

Guided Practice

• Rewrite sin in terms of cos.

sin 11 sin 80 sin 0 sin 100

• Rewrite cos in terms of sin.

cos x cos 27 cos -5 cos 64

Angle of Depression

• The angle formed by a horizontal line and a sight line going downward.

Angle of Elevation

• The angle formed by a horizontal line and a sight line going upward.

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