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Can anybody tell me what’s going on here?

Can anybody tell me what’s going on here?-example-1
User Muddassir
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1 Answer

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Explanation:

We are given a theta degree measure of sin in a specific interval. We are asked to find half of that degree measure.

The interval it ask us to find it in is between 2 pi and 5 pi over 2.

That is 360 degrees to 450 degrees. If you use reference angles, that is between the 0 degrees and 90 degrees. So that means our measure is going to be in the 1st quadrant.

Replace x with theta


\sin( (x)/(2) ) = + - \sqrt{ (1 - \cos(x) )/(2) }

We dont know cos x but we can use the pythagorean trig theorem to find cos x.


\sin {}^(2) (x) + \cos {}^(2) (x) = 1


\sin {}^(2) ( (4)/(5) ) + \cos {}^(2) (x) = 1


(16)/(25) + \cos {}^(2) (x) = 1


\cos {}^(2) (x) = 1 - (16)/(25)


\cos {}^(2) (x) = (9)/(25)


\cos(x) = (3)/(5)

Cosine in 1st quadrant is positive so 3/5 is cos x.

Replace 3/5 for cos x.


+ - \sqrt{ (1 - (3)/(5) )/(2) }


+ - \sqrt{ (2)/(10) }

The answer is


+ - \sqrt{ (2)/(10) }

User HermitCrab
by
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