CPM Homework Help : INT3 Problem 12-45

For each of the following equations, list all of the solutions without using a calculator. Draw a graph or unit circle to support your answers. Then predict the solution that your calculator will give, and use your calculator to check your prediction.

$4 \operatorname { sin } ( x ) + 2 = 0$
Step 1(a):
Subtract $2$ from both sides and divide by $4$ to solve for $\sin(x)$ .
$\sin(x)=1/2$
Step 2(a):
On a unit circle, find the two different times $\sin(x)=1/2$ . To give all of the solutions, remember that every time you go around the circle, that value occurs again. Since there are $2π$ radians in a circle, add $2πn$ to each solution.
Answer (a):
$x = \frac{7\pi}{6}+2{\pi}n,\;\frac{11\pi}{6}+2{\pi}n$

$2\cos(x)=\sqrt{3}$
Hint (b):
Use the same method as part (a).
Answer (b):
$x = \frac{\pi}{6}+2{\pi}n,\;\frac{11\pi}{6}+2{\pi}n$

$\operatorname { tan } ( x ) + 1 = 0$
Hint (c):
Use the same method as part (a). How is the tangent function different from the sine function?

$4 \operatorname { cos } ( x ) - 4 = 0$
Answer (d):
$x=2\pi{n}$
Remember to check your answers with your calculator!

Compute without a calculator