Question

How do you simplify `cos(t-pi/2)`?

Answer 1

sint

Explanation:

We can use the appropriate `color(blue)"addition formula"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(cos(A-B)=cosAcosB+sinAsinB)color(white)(a/a)|)))`

`rArrcos(t-pi/2)=costcos(pi/2)+sintsin(pi/2)`

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(cos(pi/2)=0 " and " sin(pi/2)=1)color(white)(a/a)|)))`

`rArrcostcos(pi/2)+sintsin(pi/2)=0+sint`

`rArrcos(t-pi/2)=sint`

This is a useful result and worth memorising for future use.

Answer 2

`cos(t-pi/2)`

`=cos(-(pi/2-t))`

`=cos(pi/2-t)" as "cos(-theta)=costheta`

`=sint" as "cos(pi/2-alpha)=sinalpha`