How do you simplify cos(t-pi/2)cos(tπ2)?

2 Answers
Aug 8, 2016

sint

Explanation:

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

Sep 21, 2016

cos(t-pi/2)

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

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

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