# Trigonometric Functions and Exact Value

**Topics:**Trigonometric functions, Trigonometry, Law of cosines

**Pages:**5 (543 words)

**Published:**September 14, 2013

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]

6-1 Inverse Trig Functionsp. 468: 1-31 odd

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]

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]

6-2 Inverse Trig Functions Continuedp. 474:1-41 odd

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 Trig Identities Worksheet: 1-6 all, 9, 13, 15, 19

I. Reciprocal Identities

[pic]

II. Quotient Identities

[pic]

III. Pythagorean Identities

[pic]

Simplify each expression.

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

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

7. [pic]

6-3 Trig Identitiesp. 480: 1-29 odd, omit 3

I. Guidelines for Verifying Trig Identities

A. Begin with the most complicated side

B. Work on one side only

C. Rewrite sums or differences of quotients as one single quotient D. Rewrite in terms of sine and cosine only

E. Factor ( GCF or Difference of Squares)

F. Multiply ( Foil or Distributive Property)

Verify each identity.

1. [pic]2. [pic]

3. [pic]4. [pic]

5. [pic]6. [pic]

7. [pic]

6-4 Sum and Difference Formulasp. 491: 1-23 odd, 29, 31

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]

6-5 Double-Angle and Half-Angle Identitiesp. 501: 1-5 odd, 13-17 odd, 21, 51, 53

I. Double Angle Identities

[pic]

II. Half Angle Identities

[pic]

where + or – is determined by [pic]

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]

6-7 Trig Equations (I)p. 511: 1-29 odd

Solve each equation for [pic].

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

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

7. [pic]8. [pic]

6-8 Trig Equations (II)p. 518: 1-19 odd, 25

I. Solving Trig Equations

A) Set trig function equal to a numerical value

B) Apply trig identities to rename expression in terms of one trig function C) Factor:

1. GCF

2. Product of binomials

D) Divide [pic] to produce [pic]

Solve for [pic].

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

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

7. [pic]8. [pic]

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