### Home > CCA2 > Chapter 8 > Lesson 8.3.2 > Problem8-155

8-155.
1. For each equation, find two solutions 0 ≤ x < 2π, which make the equation true. No calculator should be necessary. Homework Help ✎

1. cos x = −

2. tan x =

3. sin x = 0

4. cos x =

$\text{Recall that } \cos \left( \frac{\pi}{6}\right) = \frac{1}{2}, \text{ so the reference angle will be 30°.}$

In which quadrants is cosine negative? Sketch a unit circle with right triangles with 30° angles at the origin in the second and third quadrants. What are the circular angles?

x = 120° and 240°

Now convert the angles into radians.

$120\left(\frac{\pi}{180}\right)\ \ \ \ \ \ \ \ 240\left(\frac{\pi}{180}\right)$

$x = \frac{2{\pi}}{3}, \frac{4{\pi}}{3}$

See part (a).

If sin(x) = 0, x = 0.

x = 0

Remember the side ratios of 45° right triangles.