SOLUTION: Question Part Points Submissions Used 1 0/1 1/5 Total 0/1 Find the exact value of the expression in terms of x with the help of a reference triangle. sin(cos−1(3

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Question 1128737: Question Part
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Find the exact value of the expression in terms of x with the help of a reference triangle.
sin(cos−1(3 − x))
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
In the expression "sin(cos-1(3 - x))"
the "cos-1" or part refers to the inverse cosine function,
so is an angle , between and
(or between and if you want to visualize angles in degrees)
whose cosine is .
Those angles would have a non-negative sine, so .
Using the trigonometric identity ,
,
,
,
, and

We are looking for a non-negative result, so


NOTE:
Of course is not defined as a real number for all values of .
It must be or .
That is the domain of the function,
but that is probably not expected as part of the answer.
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