SOLUTION: Use the addition and subtraction formulas to simplify cos(x-{{{3PI/2}}}). a. cos x b. sin x c. -cos x d. -sin x

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Question 73910This question is from textbook
: Use the addition and subtraction formulas to simplify cos(x-3PI%2F2).
a. cos x
b. sin x
c. -cos x
d. -sin x
This question is from textbook

Answer by bucky(2100) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify cos(x-3PI%2F2)
.
The reduction formula that you are looking for is:
.
cos%28alpha+-+beta%29=+cos%28alpha%29%2Acos%28beta%29+%2B+sin%28alpha%29%2Asin%28beta%29
.
For this problem alpha+=+x and beta+=+3pi%2F2.
.
All you now have to do is to make the appropriate substitutions into the formula to get:
.
cos%28x+-+3pi%2F2%29+=+cos%28x%29%2Acos%283pi%2F2%29+%2B+sin%28x%29%2Asin%283pi%2F2%29
.
Now recognize that 3pi%2F2+=+270degrees. Thinking in terms of degrees may make it easier for
you to visualize that cos%283pi%2F2%29=cos%28270%29+=+0 and sin%283pi%2F2%29+=+sin%28270%29+=+-1.
.
Make these substitutions into the formula and you get:
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cos%28x+-+3pi%2F2%29+=+cos%28x%29%2A0+%2B+sin%28x%29%2A%28-1%29
.
On the right side the multiplication by zero makes the first term disappear and the multiplication
by -1 in the second term makes it become -sin(x). So the answer to this problem is:
.
cos%28x-3pi%2F2%29+=+-+sin%28x%29
.
Answer d is the correct selection
.
Hope this problem makes you aware of how the reduction formula for the cosine of the difference
between two angles works.