TRIG EQUATIONS & IDENTITIES QUIZ

Please show all steps / reasoning. Circle final answers.

1. Algebraically solve each equation on .

(a)

2. Algebraically solve on , and provide a general solution.

3. Consider the equation , on .

(a) Explain how you could solve this equation graphically, by first setting the equation to 0.

(b) Solve graphically. Provide a sketch of the graph obtained here – be sure to label the solutions as they relate to

the graph, and provide the scale used.

(c) State the general solution to the equation.

(d) Bonus – Use the appropriate identity to provide

a complete algebraic solution to the equation.

Separate Paper

(b)

4

3

4

1

2

1

2

2

30 6 36 % Identities on scrap

Total Name:

4. Consider the equation .

(a) State the non-permissible values, in radians.

5. Write each expression as a single trigonometric function:

(a) (b) (c) (d)

6. If and , evaluate:

(a) (b)

(b) Verify that this equation is true using an angle .

Show calculators / calculator entries.

(c) PROVE the identity. (Separate paper)

2

4

1

1

3 15

1 1 1 1

2 2

4

4

7. Find the exact value of (a) (b)

8. Prove the identity: Separate Paper

9. Prove the identity: Show work below

10. Simplify using a

difference identity.

LS

RS

15

2 1

3

2 2

3

4

Math 30-1 – Trigonometry II Relevant Test STUDY QUESTIONS

1. Solve on . Where possible, state solutions as exact values, in terms of .

Otherwise, round answers to the nearest hundredth of a radian. Finally, provide a general solution.

2. Prove the following identities:

(a) (b)

(c)

3. Find the exact value of .

4. Given , where , find the exact value of

5. If with , and with , evaluate:

(a) (b)

6. Consider the equation , on . Algebraically solve be first applying the appropriate double-

angle formula and simplifying the equation. (Hint: Get the equation in terms of either just sine or cosine, set equal to “0”, and

solve by factoring)

7. Use identities to algebraically solve the equation: , on . Verify graphically.

(Graph in degree mode and find the zeros. Match your window to the interval given, but in

degrees!