SOLUTION: 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? Sim

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?
===============
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)
=================================================================
Similarly, for:
sin (90+A)
I don't understand why the answer is still cos A instead of sin A
-------
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
------
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.
RELATED QUESTIONS
Write as a trigonometry ratio of x, with the correct sign attached: sin(90�-x) (answered by Edwin McCravy)

Write as a trigonometry ratio of A, with the correct sign attached: cosec (-A)... (answered by Alan3354)

Hello A pipe can empty a tank in 40 minutes. A second pipe with diameter twice as... (answered by math_helper,MathTherapy,greenestamps,ikleyn,Edwin McCravy)

For an angle a in the interval [0,π2) it is given that sin(a)=4/5 Determine cos(a)... (answered by htmentor,Solver92311)

I think my problem with these kinds of questions is that I�m having a hard time... (answered by jsmallt9)

I need help with these trigonometry problems... the question says "Write the following as (answered by jsmallt9)

I. Why must we reverse the direction of the inequality sign change when both sides are... (answered by richard1234)

i don understand this question:Simplify the expression. Write your answer as a power... (answered by Edwin McCravy,Athenal)

simplify the following to a single trigonometry term 1. cos 10 . cos 340 - sin 190 .... (answered by MaxWong)