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38 votes
Simplify: sin (x + 3pi/2)

User Walther
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1 Answer

7 votes
7 votes

We can use the formula for the sine of an addition of angles to answer this question:

Recall that:

sin(A + B) = sin(A) cos(B) + sIn(B) cos(A)

which in our case gives:

sin (x + 3pi/2) = sin(x) cos(3pi/2) + sin(3pi/2) cos(x)

now, we recall that 3pi/2 is one of the "special angles"of trigonometry, where the sin gives a value of -1, and the cosine, a value of "0".

Then we end up with the following:

sin(x) * (0) + (-1) cos(x) = - cos(x)

Therefore, the simplified answer is:

- cos(x) (negative cosine of x)

User Alex Ackerman
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