Question

Choose the two options which are true for all values of x

1) cos (x) = cos ( x – pie/2)
2) sin (x + pie/2) = cos (x – pie/2)
3) cos (x) = sin (x – pie/2)
4) sin (x) = sin (x + 4pie)
5) sin (x) = cos (x – pie/2)
6) sin^2 (x) + cos^2 (x) = pie

would it be 1 and 3 ??


I helps if you know the shape of the standard sine and cosine fucntion.

Also you will have to know that sin(x+A) is a horizonatal translation of A to the LEFT (obviously sin(x-A) would shift to the right)

if all else fails, pick any angle for x and realize that pi radians = 180º

lets check #3, let x= 37.6º (notice I don't pick a nice standard angle)

cos 37.6=.7922896
sin(37.6-180)=-.7922896 (opposites) so #3 is false

try the same angle in #5