10-1

cos(x+pie/2)= -sin x
cos x*cos pie/2-sin x*sin pie/2
0*cos x-sin x*1
= -sin x

To simplify these types problems, we are given six different formulas for this section.  The two main formulas we use for this section is cos(alpha+/- beta)=cos theta*cos beta-/+sin theta*sin beta and sin(theta+/- beta)=sin theta*cos beta+/- cos theta*sin beta.  For this problem, we had to show how cos(x+pie/2) is equal to -sin x.  To do this, you remember your formulas and see what replaces cos(x+pie/2) and that is cos x*cos pie/2-sin x*sin pie/2.  Cos pie/2 is on your trig chart and that equals 0.  Sin pie/2 is also on your trig chart and that equals 1.  Now you have cos x*0-sin x*1.  Cos x*0 equals 0, so -sin x*1 equals -sin x.  -sin x is your answer.