Question 566836: Show that cos(x+pi/2)= -sin x for every number x
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Show that cos(x+pi/2)= -sin x for every number x
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The best way I know how to show this is doing it graphically with a unit circle.
Note that every time you rotate angle x by π/2 radians, the reference angle changes to the complement of the angle one quadrant over and either the sin or cos switch signs, but not both.
To illustrate, here are examples:
let x=30º (we could use any angle)
sin x=sin 30º=1/2
cos(x+90)=cos120º=-1/2 (reference angle = 60º in quadrant II where cos<0)
cos(x+π/2)= -sin x
..
another example:
let x=210º
sin x=-1/2
cos(210+90)=cos300º=1/2 (reference angle = 30º in quadrant IV where cos>0)
cos(x+π/2)= -sin x
Maybe someone can show how to do it algebraically.
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