Trigonometric Identities Exercises

Trigonometric Identities Exercises

Example 1

Simplify: .

Hint

Example 2

Find

Hint

Inverse sine is limited to Quadrants I and IV.

Example 3

Find tan^-1(-1).

Hint

Inverse tangent is limited to Quadrants I and IV.

Example 4

Find .

Hint

Inverse tangent is limited to Quadrants I and IV.

Example 5

Find Give your answer in radians.

Hint

Example 6

Find sec^-1(2) in radians.

Hint

Example 7

If in Quadrant II, what is tan ɵ?

Hint

Remember ASTC. Tangent is negative in Quadrant II.

Example 8

If in Quadrant II, what is cos ɵ?

Hint

Cosine is negative in Quadrant II. He's a real bummer.

Example 9

If in Quadrant IV, what is tan ɵ?

Hint

It's all about the ASTC, yo. Tangent is negative in Quadrant IV.

Example 10

If in Quadrant II, what is sin ɵ?

Hint

Ah yes, Quadrant II. Home of the positive sine.

Example 11

If in Quadrant III, what is cos ɵ?

Hint

You know who's negative in Quadrant III? Cosine, that's who.

Example 12

If in Quadrant I, what is tan ɵ?

Hint

Everybody's positive in Quadrant I. Try using Pythagoras.

Example 13

Use a sum or difference identity to find cos(-15°).

Hint

cos(30° – 45°)

Example 14

Use a sum or difference identity to find sin(15°).

Hint

sin(45° – 30°)

Example 15

Use a sum or difference identity to find sin(255°).

Hint

sin(300° – 45°)

Example 16

Use a sum or difference identity to find sin(285°).

Hint

sin(225° + 60°)

Example 17

Use a sum or difference identity to find cos(195°).

Hint

cos(135° + 60°)

Example 18

Find tan(105°).

Hint

tan(105°) = tan(60° + 45°)

Example 19

Find tan(15°).

Hint

tan(15°) = tan(45° – 30°)