FOR NJOSH ONLY

Trigonometry Exam 4 (Due Friday, 10/21, by 9:05 am) Fall 2016

Name:

You must show ALL work to receive full credit. Please name/list the trig identity used, when appropriate.

1. Verify the identity.

2 − 𝑠𝑖𝑛2𝜃

𝑐𝑜𝑠𝜃 = 𝑠𝑒𝑐𝜃 + 𝑐𝑜𝑠𝜃

2. Use the appropriate identity to find the EXACT VALUE.

tan 10°+tan 35°

1−tan 10° tan 35°

Trigonometry Exam 4 (Due Friday, 10/21, by 9:05 am) Fall 2016

3. Find cos(𝑥 + 𝑦) if tan 𝑥 = 2 3⁄ , tan 𝑦 = 1

3⁄ , 𝑥 is in quadrant I, and 𝑦 is in quadrant III.

4. Verify the identity.

tan 𝑥 − tan 𝑦 = sin(𝑥 − 𝑦)

cos 𝑥 cos 𝑦

Trigonometry Exam 4 (Due Friday, 10/21, by 9:05 am) Fall 2016

5. Use the given information and the appropriate indentity to find the exact value of sin 2𝑥,

cos 2𝑥, 𝑎𝑛𝑑 tan 2𝑥. [Hint: Draw a reference triangle.]

cos 𝑥 = − 8

17 , 𝜋 2⁄ < 𝑥 < 𝜋

6. Use the half-angle identities to find the EXACT VALUE.

tan 75°

Trigonometry Exam 4 (Due Friday, 10/21, by 9:05 am) Fall 2016

7. Verify the identity.

sin 2𝑥 = 2 tan 𝑥

1 + 𝑡𝑎𝑛2𝑥

8. Evaluate exactly using an appropriate identity.

cos 285° + cos 195°

9. Verify the identity.

sin 𝑥 − sin 𝑦

cos 𝑥 − cos 𝑦 = − cot (

𝑥 + 𝑦

2 )