### Home > CCA2 > Chapter 12 > Lesson 12.2.2 > Problem12-111

12-111.

Without using a calculator, solve each equation below in the domain $0 ≤ x < 2π$.

1. $\sin(x)=-1$

Reference the unit circle to help solve this problem.
For which angle(s) in the circle does $\sin(x)=-1$.

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

1. $2\cos(x)-1=0$

Solve the equation for $\cos(x)$.

$\cos(x) = \frac{1}{2}$

For which angle(s) in the unit circle does $\cos(x)=\frac{1}{2}$?

1. $\tan(x)=1$

Refer to part (a).

1. $2\sin\left(x\right)=4\sin\left(x\right)+1$

How would you solve $2m = 4m + 1?$
In this case $m =$ sin$(x)$.

$x=\frac{7\pi}{6},\frac{11\pi}{6}$