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

2 Answers
Aug 8, 2016

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.

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#