Trigonometric Identities

Trigonometric Identities

•Reciprocal Identities

2

sin 1

csc

cos 1

sec

tan 1

cot

csc 1

sin

sec 1

cos

cot 1

tan

Trigonometric Identities

•Quotient Identities

3

tan sincos

cot cossin

Trigonometric Identities

•Pythagorean Identities

4

sin2 cos2 1

1 tan2 sec2

1 cot 2 csc2

Note: sin2 is (sin )2 not sin (2)

Example 5

Use trigonometric identities to transform one side of the equation into the other.

•cossec=1

•(sec+tan)(sec-tan)=1

5

Homework Practice

6

Surveying

•A surveyor is standing 50 ft from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree?

7

River Walk

• You are 200 yards from a river. Rather than walking directly to the river, you walk 400 yards along a straight path to the river’s edge. Find the acute angle ө between this path and the river’s edge.

8

Skateboarding

•Find the length c of the skateboard ramp.

9