Why does cos A = sin (90 - A)?

Answer 1

Because
sin(a - b) = sin a cos b - cos a sin b so
sin(90 - A) = sin 90 cos A - cos 90 sin A
sin(90 - A) = 1(cos A) - (0)sin A
sin(90 - A) = cos A

^_^

Answer 2

Sin A Cos A

Answer 3

Sin 90-a

Answer 4

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RE:
Why does cos A = sin (90 - A)?

Answer 5

You have a right triangle, right?

One angle measures 90º.

If the other measures A, the third angle must measure (90-A), since the sum of all angle measures in a triangle is 180º.

Now there are three sides, L1, L2 and H. Let's arbitrarily set L1 as the side adjacent to angle A. That is, A has sides L1 and H. Then L2 is opposite A by default.

It just so happens then, that L2 must be adjacent to the angle we're calling (90-A).

Sin = Opposite/Hypoteneuse. Cos=Adjacent/Hypoteneuse.
Sin (A) = L2/H. Cos (90-A) = L2/H.
If a=c and b=c, a=b.

sin (A) = cos (90-A)

Q.E.D.

Answer 6

Cos A is defined as base/hypotenuse in a right angle triangle where A is the angle shared by base with 90 degree. Sin A is defined as perpendicular/hypotenuse. If we consider the other angle it would be 90-A and Sin (90-A) will be perpendicular/hypotenuse. So turning the triangle, base becomes perpendicular as base angle changes from A to 90-A.

Answer 7

cos A = sin(90-A)
assume A = 90 degree
so cos 90 = 0

o.k sin(90-A) = sin(90-90)= sin(0)=0

its not a prove, I don't remeber the proof

Answer 8

Well, if you look at a right triangle with hypotenuse c and legs a and b, you get the sine of angle A = a/c. The cosine of angle 90-A is adjacent/hypotenuse, or a/c. So sin A = cos(90-A). Let A = 90-B. Then sin(90-B) = cos(90-(90-B)) = cos(B)

Answer 9

Do you know how to draw the curve?

sine is an odd function
cosine is an even function

ie

sin(-A)=-sinA
cos(-A)=cosA]

f(x+a)=f(x) ,moves 'a' units towards left

If u observe the two curves youll see that
cosA=sin(A+90)


now you should know that


sinB=sin(180-B)....this can be deduced by the observation of the curve...



sin(90+A)=sin(180-(90+A))
=sin(90-A)

Answer 10

mamaroy has the simplest ( and correct) answer

If you have a right triangle, and you label one of the angles A, the other angle will be 90-A ( call it B).

The leg opposite A is the side adjacent to B and the side opposite B is the side adjacent to A.
Cos A = (adjacent to A)/hypoteneuse = (opposite B)/hypoteneuse = sin B = sin(90-A)