Question

PROVED THAT.
sin90=1
cos90=0

​

Answer 1

Answer:

We know that sin0=p/h

if angle is of 90°

in a right angle triangle

then

perpendicular is equal to the hypothesis

so sin90=p/p=1

and we know that

cosO=b/h

if theeta is 90°

then in the right angle triangle

base is not present so

cos90=0/h=0

Answer 2

Answer:

Step-by-step explanation:

Use a triangle within the unit circle (length of the hypotenuse is equal to the radius of the circle is equal to 1). Because sine is defined as the opposite over the hypotenuse, it is easy to show that as the the sine of any angle is equal to the length of the opposite side divided by 1, which is simply equal to the length of the opposite side. When the angle is equal to 90 degrees, the opposite side is coincident with the hypotenuse - they are of equal length. Therfore, opposite/hypotenuse = 1/1 = 1.

Therefore, sin(90) = 1

Imagine a right angled triangle which has of course 3 sides, Which we will call "x" for the horizontal side, "y" for the vertical side and "h" for the third side (hypotenuse).

The angle concerned is that formed between the hypotenuse, "h" and the horizontal side "x"

The cosine of this angle is defined as the length of "x" divided by the length of "h"

Now imagine that the length of "x" is gradually reduced.

The angle becomes greater for decreasing values of "x"

i.e. the hypotenuse becomes steeper.

Therefore the value of "x" divided by "h" becomes less

If you take this to its extreme then you would have a triangle which had "x" = 0 and the values of "h" and "y" would be the same. (This would in practise be simply a vertical line)

If however you imagine this as still being a triangle it would have two angles of 90 degrees and one of 0 degrees.

The angle we are concerned with is 90 degrees.

since the value of "x" = 0

The cosine of our angle is 0 divided by the value of the hypotenuse "h"

0 divided by any quantity is 0  

Therefore the answer (x/h) is 0