Question

How do you simplify `sin(t+pi/2)`?

Answer 1

`cost`

Explanation:

Using the appropriate `color(blue)"addition formula"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(sin(A+B)=sinAcosB+cosAsinB)color(white)(a/a)|)))`

`rArrsin(t+pi/2)=sintcos(pi/2)+costsin(pi/2)`

now `cos(pi/2)=0" and " sin(pi/2)=1`

`rArrsintcos(pi/2)+costsin(pi/2)=sint(0)+cost(1)`

`rArrsin(t+pi/2)=cost`