CPM Homework Help : A2C Problem 13-46

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Home > A2C > Chapter 13 > Lesson 13.1.3 > Problem 13-46

13-46.

Solve each equation for $0°≤θ<360°$ , or if you prefer, $0 ≤ θ < 2π$ . You may need your calculator, but remember that it only gives one answer.

$\sin(\theta)=0.5$
Step 1(a):
Use inverse sine on your calculator to find one solution.
sin⁻¹ $(0.5) =$ θ
Partial Answer (a):
It should tell you the answer is $30°$ .
Step 2(a):
Draw a unit circle to find the other angle that makes sin(θ) $= 0.5$ . The sine function is positive in quadrants I and II, so draw a reference angle of $30°$ in each quadrant.
Answer (a):

$\cos(\theta)= -0.5$
Hint (b):
Follow the steps in part (a).
Answer (b):

$4\tan(\theta)- 4 = 0$
Step 1(c):
First solve the equation for tan(θ).
tan(θ) $= 1$ .
Step 2(c):
Follow the steps in part (a).
Answer (c):
$45°$ and $225°$

$3\sin^2(\theta)= 1$
Step 1(d):
First solve the equation for sin(θ).
$\sin(\theta) \ = \pm \sqrt{\frac{1}{3}}$
Step 2(d):
Follow the steps in part (a). There are $4$ solutions.

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