CPM Homework Help : CCA2 Problem 12-111

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12-111.

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

$\sin(x)=-1$
Hint (a):
Reference the unit circle to help solve this problem.
For which angle(s) in the circle does $\sin(x)=-1$ .
Answer (a):
$x=\frac{3\pi}{2}$

$2\cos(x)-1=0$
Hint (b):
Solve the equation for $\cos(x)$ .
Step 1(b):
$\cos(x) = \frac{1}{2}$
Step 2(b):
For which angle(s) in the unit circle does $\cos(x)=\frac{1}{2}$ ?

$\tan(x)=1$
Hint (c):
Refer to part (a).

$2\sin\left(x\right)=4\sin\left(x\right)+1$
Hint (d):
How would you solve $2m = 4m + 1?$
In this case $m =$ sin $(x)$ .
Answer (d):
$x=\frac{7\pi}{6},\frac{11\pi}{6}$

Compute without a calculator

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