SOLUTION: The value of b that would make the equation costheta =sin (theta +b) true is A) pi B) -pi C)pi/2 D)-pi/2

Algebra ->  Trigonometry-basics -> SOLUTION: The value of b that would make the equation costheta =sin (theta +b) true is A) pi B) -pi C)pi/2 D)-pi/2      Log On


   

Question 1091112: The value of b that would make the equation costheta =sin (theta +b) true is
A) pi
B) -pi
C)pi/2
D)-pi/2
Found 2 solutions by math_helper, josmiceli:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
C)
cos%28theta%29+=+sin%28theta%2Bpi%2F2%29
This is an identity you should memorize. Cosine leads Sine by 90 degrees (pi/2 radians).
cos%280%29+=+sin%28pi%2F2%29+=+1
---
cos%28pi%2F2%29+=+sin%28pi%29+=+0
---
cos%28pi%29+=+sin%283pi%2F2%29+=+-1+
---
cos%283pi%2F2%29=+sin%282pi%29+=+0+
---
etc.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Since +theta+ isn't specified, the choce
must hold true for any +theta+, so I'll
say +theta+=+0+ radians
---------------------------------------
A)
+cos%280%29+=+sin%28+0+%2B+pi+%29+
+1+=+0+ NOT TRUE
B)
+cos%280%29+=+sin+%280+-+pi+%29+
+1+=+0+ NOT TRUE
C)
+cos%280%29+=+sin%28+0+%2B+pi%2F2+%29+
+1+=+1+ TRUE
D)
+cos%280%29+=+sin%28+0+-+pi%2F2+%29+
+1+=+-1+ NOT TRUE
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The answer is C)