# A Series of Trigonometry Problems

I have some trig questions I need help with:

1. find the number of degrees in the measure of the smallest positive angle that satisfies the equation 2cos(x) + 1 = 0

2. In the interval 0 degrees < (or equal to) x < (or equal to) 360 degrees, sin (x) = -1. Find the number of degrees in the measure of angle x

3. If x is a positive acute angle and 2cos(x) + 3 = 4, find the number of degrees in the measure of angle x.

4. If angle x is in Quadrant III and 2tan(x) - 3=3tan(x) - 4, find the number of degrees in the measure of angle x.

5. In the interval 0 degrees < (or equal to) x < (or equal to) 360 degrees, how many values of x satisfy the equation 3sin (squared) (x) + sin(x) - 2 = 0?

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#### Solution Preview

1. 2cos(x)+1 = 0

Subtract both sides of the equation by -1 to get:

2cos(x)=-1

Divide both sides of the equation by 2 to get:

Cos(x)=(-1/2)

X should be 120 degrees

2. Sin(x)=-1

x ...

#### Solution Summary

This solution explains how to solve a series of trigonometry problems by showing how the problems should be solved step-by-step.