Problem Statement

Use the figure below to find all angles between 0 and 2π satisfying the given condition.

 
Step 1

Question Sequence

Question 1

Recall that csc(θ) = is

Incorrect
Correct

Question 2

And thus, sin(θ) = is

Incorrect
Correct

 
Step 2

Question Sequence

Question 3

Since and we are given that , if follows that sin(θ)=

2
Incorrect
Correct

 
Step 3

Question Sequence

Question 4

The figure shows that in the first quadrant, when θ = .

2
Correct.
Incorrect.

Question 5

The only other quadrant where sin(θ) is positive is the quadrant.

Correct.
Incorrect.

 
Step 4

We need a second quadrant angle, , for which .

Question Sequence

Question 6

From the figure,

θ =

Correct.
Incorrect.

Question 7

Thus, for the following values of θ (0 < θ < 2π).

θ = and

Correct.
Incorrect.