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 ntion.
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
To check option #5, we substitute x = 37.6º in the equation:
sin(x) = cos(x - π/2)
sin(37.6º) = cos(37.6º - π/2)
Using the angle subtraction identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b), we have:
sin(37.6º) = cos(37.6º)cos(π/2) + sin(37.6º)sin(π/2)
sin(37.6º) = cos(37.6º)(0) + sin(37.6º)(1)
sin(37.6º) = sin(37.6º)
Since both sides of the equation are equal, option #5 is true.
Therefore, the two options that are true for all values of x are:
1) cos(x) = cos(x - π/2)
5) sin(x) = cos(x - π/2)