Question

Why does sin(90 + angle ) =cos angle because on using above property it should br - cos angle?

Answer 1

See below.

Explanation:

The answer comes from the trig identity development:

`sin (90 + x) = sin 90 * cos x + cos 90 * sin x`

Note that

`sin 90 = 1" "` and `" " cos 90 = 0`

Therefore:

`sin (90 + x) = cos x`

In below example, the complementary arc gives a negative cos value.

`sin (x - 90) = sin x * cos 90 - sin 90 * cos x`

Note that:

`cos 90 = 0 " "` and `" " sin 90 = 1`

Therefore:

`sin (x - 90) = - cos x`