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

8-155.

For each equation, find two solutions $0 ≤ x < 2π$, which make the equation true. No calculator should be necessary.

1. $\cos x = −\frac { 1 } { 2 }$

Recall that $\cos \left( \frac{\pi}{6}\right) = \frac{1}{2},$ 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.

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

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

1. $\tan x =\frac { \sqrt { 3 } } { 3 }$

See part (a).

1. $\sin x = 0$

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

$x = 0$

1. $\cos x =\frac { \sqrt { 2 } } { 2 }$

Remember the side ratios of $45°$ right triangles.