Handwrite answers on pieces of papers, and take picture of them, I really need to get a hundred, please check your answers, after you do them.

Precalculus

Final Exam

Prof. Ockay

Directions: Do all work and put all answers on the blank sheets,

NOT on the test. Use correct notation, state any formulas used, and

show your work.

1. Sketch a reasonable graph of (7 points)

2. Solve the equation: 6 (round the answer to 4 decimal

places. (5 points)

3. Graph

. Clearly label all intercepts and asymptotes.

(8 points)

4. Write as a sum, difference, or product of logarithms: (5 points)

log

5. Graph each function clearly label the intercepts and

asymptotes: (3 points each)

a)

b) ln

6. Find the exact value of cos , if tan

(6 points)

3

and sin .

7. Graph one period of the function cos 3 . Include

all intercepts. Label the values for which the function has its

maximum or minimum values. (8 points)

8. Simplify: cos

sin

(7 points)

cos

9. Verify the identity: cos

sin

sin

cos (8 points)

10. Find all solutions of the equation in the interval [ :

(give the answer in radians)

sin

(8 points)

11. Given sin

, with , find the exact value of

cos and sin using the double angle identities.

(8 points)

12. Give the exact value of tan (arcsin ). (8 points)

13. Rewrite the expression so that it is not in fractional form:

tan

csc cot

14. Let find and simplify

(8 points)

(8 points)