CPM Homework Help : INT3 Problem 12-25

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12-25.

For each of the following equations, what are the solutions that lie in the domain $0\le x<2\pi$ ?

$2 \operatorname { sin } ( x ) - 1 = 0$
Hint (a):
$\text{For the equation to be true, sin(x) must= }\frac{1}{2}.$
Hint 2 (a):
You can either draw a unit circle to find all possible solutions, or solve the equation graphically.
Answer (a):

$2 \operatorname { cos } ( x ) = - \sqrt { 3 }$
Hint (b):
In what quadrants is cos(x) negative?
Answer (b):

$2 \operatorname { sin } ( x ) = \sqrt { 2 }$
Hint (c):
$\text{When does sin(x)= }\frac{\sqrt{2}}{2}?$

$\operatorname { cos } ( x ) = 1$
Hint (d):
Picture a unit circle. At what angle is the adjacent side the same length as the hypotenuse?

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