A satellite dish is aligned such that it makes an angle x with the horizontal. It is known that cos x = -3/5 and x lies in the third quadrant. Given that precision is required for signal locking, what is the sine of half the angle of elevation (x/2)?
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Correct answer: A
Explanation
cos x = -3/5
x is in the third quadrant.
Since x is in the third quadrant,
180° < x < 270°
90° < x/2 < 135°
x/2 will be in the second quadrant, where sin(x/2) is positive.
sin(x/2) = √[(1 − cos x)/2]
Substituting cos x = -3/5:
sin(x/2) = √[(1 + 3/5)/2]
= √[(8/5)/2]
= √(4/5)
= 2/√5
sin(x/2) = 2/√5