Question 1108426: Write as a trigonometry ratio of A, with the correct sign attached:
sin(90-A)
I don't understand why the answer is cos A instead of sin A, could someone please explain?
Similarly, for:
sin (90+A)
I don't understand why the answer is still cos A instead of sin A
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Write as a trigonometry ratio of A, with the correct sign attached:
sin(90-A)
I don't understand why the answer is cos A instead of sin A, could someone please explain?
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90-A is the complement of A.
cosine is the complement of the sine.
It's a definition.
You can confirm it using the sum of angles:
sin(90-A) = sin(90)cos(A) - sin(A)cos(90) = cos(A)
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Similarly, for:
sin (90+A)
I don't understand why the answer is still cos A instead of sin A
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Plot the terminal point of an angle on the unit circle.
The sin is y/r = y
Rotate the point 90 degs CCW, and the y value is now x.
x/r = cosine
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And, as above:
sin(90+A) = sin(90)cos(A) + sin(A)cos(90) = cos(A)
The signs, + or minus, can be different depending on angle A.
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