Question

Verify the identity. cos(x+pi/2) = -sin x
please help!

Answer 1

There is an identity you can use, are you familiar with the co-function identities?

Answer 2

Using the identities for sine you may arrive at proving the equation

Answer 3

i think i have it hold on

Answer 4

oh i got it @Johnbc but what do i do with the negative sign

Answer 5

Well if you notice the cofunction of Sine would be this:\[Sin \theta=\cos(\frac{ \pi }{ 2 }- \theta)\]

Answer 6

where our original shows that there is a plus in-between the angle and the pi/2 so we have to remove a multiple of -1 to get to: \[Sin \theta= - Cos (-\frac{ \pi }{ 2 } + \theta) \]

Answer 7

so if you divide both sides by -1 and re-arrange whats inside the cosine you get

Answer 8

\[-\sin \theta = \cos(\theta - \frac{ \pi }{ 2}) \]
which now looks like your original function?

Answer 9

cos(x+pi/2)= -sinx

Use the cosine angle addition rule: cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

= cos(x)cos(pi/2)-sin(x)sin(pi/2)

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

= -sin(x)