Question

What is `sin(x+pi/2)`?

Answer 1

cos x

With `pi/2` add to any angle measure, sin changes to cos and vice- versa. Hence It would change to cosine and since the angle measure falls in the second quadrant, hence sin(x+`pi/2`) would be positive.

Alternatively sin(x+`pi/2`)= sin x cos `pi/2` + cos x sin`pi/2`. Since cos `pi/2` is 0 and sin`pi/2` is 1, it would be equal to cosx