CPM Homework Help : PCT Problem 4-124

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4-124.

Find all values of $θ$ that satisfy the equations below. Assume $0 ≤ θ ≤ 2\pi$ . Use exact values.

$\text{sin }θ =-\frac { 1 } { 2 }$
Hint (a):
Draw a unit circle. In which quadrants is sine negative?

$\text{cos }θ =\frac { \sqrt { 2 } } { 2 }$
Hint (b):
1. What special angle is this?
2. In which quadrants is cosine positive?

$\text{tan }θ =\sqrt { 3 }$
Hint (c):
$\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}$
$\tan(\theta)=\frac{\sqrt{3}}{1}=\frac{\sqrt{3}/2}{1/2}$

$\text{csc }θ =\sqrt { 2 }$
Step (d):
$\frac{1}{\sin(\theta)}=\frac{\sqrt{2}}{1}$

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