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

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Answer 1 · 2018-06-27T02:54:30

See below.

The answer comes from the trig identity development:

$sin (90 + x) = sin 90 \cdot cos x + cos 90 \cdot sin x$ $sin (90 + x) = sin 90 * cos x + cos 90 * sin x$

Note that

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

Therefore:

$sin (90 + x) = cos x$ $sin (90 + x) = cos x$

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

$sin (x - 90) = sin x \cdot cos 90 - sin 90 \cdot cos x$ $sin (x - 90) = sin x * cos 90 - sin 90 * cos x$

Note that:

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

Therefore:

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