Trigonometric Identities



Trigonometric Identities

I. Pythagorean Identities

A. [pic]

B. [pic]

C. [pic]

II. Sum and Difference of Angles Identities

A. [pic]

B. [pic]

C. [pic]

D. [pic]

E. [pic]

F. [pic]

III. Double Angle Identities

A. [pic]

B. [pic]

=[pic]

=[pic]

C. [pic]

IV. Half Angle Identities

A. [pic]

B. [pic]

C. [pic]

Inverse Trig Functions

A. [pic]

B. [pic]

C. [pic]

Find the exact value of each expression

1. [pic] 2. [pic] 3. [pic]

4. [pic] 5. [pic] 6. [pic]

Use a calculator to find each value.

7. [pic] 8. [pic] 9. [pic]

Find the exact value of each expression.

10. [pic] 11. [pic] 12. [pic]

I. Inverse Trig Functions

A. [pic]

B. [pic]

C. [pic]

Find the exact value of each expression.

1. [pic] 2. [pic] 3. [pic]

4. [pic] 5. [pic] 6. [pic] 7. [pic]

Find the exact value of each.

8. [pic] 9. [pic] 10. [pic]

Use a calculator to find each value.

11. [pic] 12. [pic]

Trigonometric Identities

Simplify each expression.

1. [pic] 2. [pic] 3. [pic]

4. [pic] 5. [pic] 6. [pic]

7. [pic]

Verify each identity.

1. [pic] 2. [pic]

3. [pic] 4. [pic]

5. [pic] 6. [pic]

7. [pic]

Sum and Difference Formulas

I. Sum and Difference Identities

A. [pic]

B. [pic]

C. [pic]

D. [pic]

E. [pic]

F. [pic]

Find the exact value of each expression.

1. [pic] 2. [pic] 3. [pic] 4. [pic]

5. [pic] 6. [pic]

Find each of the following.

a) [pic] b) [pic]

7. [pic]

[pic]

8. Verify:

[pic]

Double-Angle and Half-Angle Identities

Find the exact value of each expression.

a) [pic] b) [pic] c) [pic]

1. [pic] 2. [pic]

Use the half angle identity to find each exact value.

3. [pic] 4. [pic]

Find the exact value.

5. [pic] 6. [pic]

Trig Equations (I)

Solve each equation for [pic].

1. [pic] 2. [pic] 3. [pic]

4. [pic] 5. [pic] 6. [pic]

7. [pic] 8. [pic]

Trig Equations

Solve for [pic].

1. [pic] 2. [pic] 3. [pic]

4. [pic] 5. [pic] 6. [pic]

7. [pic] 8. [pic]

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