 # Trigonometry Questions

## Question

1. Solve the inequality sin x > −1/ 2 . Express the exact answer in interval notation, restricting your attention to −π ≤ x ≤ π.

2. The voltage V in an alternating current source has amplitude 220√2 and frequency f = 50 Hertz. Find a sinusoid which models this voltage. Assume that the phase is 0.

3. A hiker determines the bearing to a lodge from her current position is S40 degrees W. She proceeds to hike 2 miles at a bearing of S35 degrees E at which point she determines the bearing to the lodge is S60 degrees W. How far is she from the lodge at this point? Round your answer to the nearest hundredth of a mile.

4. Assume you know of a triangle with sides a = c = 31 and angle β = 62 degrees. What is the area of the triangle?

## Solution Preview

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3. This is a problem for the law of sines.

It states that sin(α)/a=sin(β)/b in ANY triangle. Where a and b must be opposites side of triangle to the angles α and β.
So, we see, that after travelling 2 miles she changed bearing on 20 degrees. So, A=2 and α=20.
Now, we need another angle. It will be the difference between S40W and S35E.
This difference is 75 degrees.
Now, we can construct the law of sines:
Sin(20)/2=sin(75)/x
X=2*sin(75)/sin(20)=5.648=5.65 miles...
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