SOLUTION: Given the function f(x) = a sin x + q a) What is the maximum value of f(x)? For what values of x does this occur? b) What is the minimum value of f(x) ? For what values of x

Algebra ->  Trigonometry-basics -> SOLUTION: Given the function f(x) = a sin x + q a) What is the maximum value of f(x)? For what values of x does this occur? b) What is the minimum value of f(x) ? For what values of x      Log On


   



Question 860361: Given the function f(x) = a sin x + q
a) What is the maximum value of f(x)? For what values of x does this occur?
b) What is the minimum value of f(x) ? For what values of x does this occur?


Can you please help ? Thank you very much

Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Given the function f(x) = a sin x + q
a) What is the maximum value of f(x)?
a + q
For what values of x does this occur?
x+=+pi%2F2+%2B-+2n%2Api, n = 0,1,2,3...
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b) What is the minimum value of f(x)?
q - a
For what values of x does this occur?
x+=+3pi%2F2+%2B-+2n%2Api, n = 0,1,2,3...

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The function +sin%28x%29+ varies between +1+ and +-1+
so, the maximum that +a%2Asin%28x%29+%2B+q+ can be is:
+a%2A1+%2B+q+=+a+%2B+q+
This occurs when +x+=+%28+4n+%2B+1+%29%2A%28+pi%2F2+%29+ where n = 0,1,2,3,4, . . .
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The minimum that +a%2Asin%28x%29+%2B+q+ can be is:
+a%2A%28-1%29+%2B+q+=+-a+%2B+q+
This occurs when +x+=+%28+4n+%2B+3+%29%2A%28+pi%2F2+%29+ where n = 0,1,2,3,4, . . .
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