precalc homework

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1. Evaluate the following:

a. sec−1⎛⎜−2⎞⎟

⎝ 3⎠

b. csc−1(−2)

c. cot−1⎜⎛− 3⎞⎟

⎝ 3 ⎠

2. Construct a graph of y= cotx . Label at least three points on the graph and use dotted lines for the asymptotes.

3. Construct the graph of y= cot−1x . Label at least three points on the graph and use dotted lines for the asymptotes.

4. Solve the following equations and express solutions in the interval [0, 2π]

a. 2sinθ+7= 6

b. tan2θ=

c. 2cos2θ−cosθ−1=0

5. Express a general formula for all of the solutions.

a. cosθ=

b. tanθ=

−

1

3

c. sin(4θ)=

d. sec⎛⎜θ⎞⎟=− 2

⎝3⎠

6. Solve each equation on the interval 0 ≤θ< 2π.

a. 2cos2θ=1+sinθ

b. 2cos2θ−7cosθ+3=0

c. 3secθ+1=7

d. sinθ= cosθ