### Home > INT3 > Chapter 12 > Lesson 12.1.3 > Problem12-45

12-45.
1. 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. Homework Help ✎

1. 4sin(x) + 2 = 0

2. 2cos(x) =

3. tan(x) + 1 = 0

4. 4cos(x) – 4 = 0

Subtract 2 from both sides and divide by 4 to solve for sin(x).

sin (x) = 1/2

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.

$x = \frac{7\pi}{6}+2{\pi}n,\;\frac{11\pi}{6}+2{\pi}n$

Use the same method as part (a).

$x = \frac{\pi}{6}+2{\pi}n,\;\frac{11\pi}{6}+2{\pi}n$

Use the same method as part (a). How is the tangent function different from the sine function?

$x=2\pi{n}$