You could actually prove this for yourself by using one of the expansion formulas
recall sin(A+B) = sinAcosB + cosAsinB
so
sin(x+90) = sinx cos90 + cosx sin 90
= sinx (0) + cosx (1)
= cos x
test it with some angles you should know
let x = 30°
sin (30+90)
= sin 120
= √3/2
= cos 30
= √3/2
see if you can find the equivalent of cos(x+90)
sin(x+90) = ?
cos(x+90) = ?
Would the first equal like -sin(x)?
Would the second equal uh -cos(x)?
I'm not quite sure :/
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