Question

Use standard trig identities to show that cos(x+(pi/2))=-sin(x). For each step indicate which identity you used.

Answer 1

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

Answer 2

more commonly just the - in between.

Answer 3

using the sum of angles theorem

\[\cos(x + \pi/2) = \cos(x)\times \cos(\pi/2) - \sin(x) \times \sin(\pi/2)\]

cos(pi/2) = 0 and sin(pi/2) = 1

= 0 - sin(x) x 1
= -sin(x)