CPM Homework Help : INT3 Problem 10-188

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10-188.

Solve each equation for $0^\circ\leθ<360^\circ$ . You may need your calculator, but remember that your calculator only gives one answer. Most of these problems have more than one answer. Think about all four quadrants of a graph.

$\operatorname { sin } ( \theta ) = 0.5$
Hint (a):
Where is the $\text{sin}θ = 0.5$ ? Remember sin is the $y$ -value. What would $θ$ be at those places?
Answer (a):
$θ = 30^\circ$ or $150^\circ$

$\operatorname { cos } ( \theta ) = - 0.5$
Hint (b):
Where is the $\text{cos}θ = −0.5$ ? Remember cos is the $x$ -value. What would $θ$ be at those places?

$4 \operatorname { tan } ( \theta ) - 4 = 0$
Hint (c):
Solve for the $\text{tan}θ$ . Draw a unit circle. Where is the $\text{tan}θ$ of that value?

$3 \operatorname { sin } ^ { 2 } ( \theta ) = 1$
Hint (d):
Use your calculator to get one of the values. Then use symmetry to get the other 3 values. There are 4 values because when you take the square root of both sides the answer would be plus or minus!

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