# Help with Cosine Function

• Sep 23rd 2012, 07:14 AM
ubhutto
Help with Cosine Function
What function is y = cos(x + π) equal to

can you also explain the answer

thanks
• Sep 23rd 2012, 07:32 AM
MarkFL
Re: Help with Cosine Function
Use the angle-sum identity for cosine:

$\cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)$

You may also think of the unit circle. Pick an arbitrary point on the circle. The counter-clockwise angle to the radius at this point as measured from the positive x-axis is the angle $\theta$. The x-coordinate of this point is $\cos(\theta)$. To add $\pi$ radians to this angle, go to the point on the opposite side of the circle, on the other end of the diameter. Can you see what relation the new x-coordinate will always have with the original?
• Sep 23rd 2012, 07:43 AM
SworD
Re: Help with Cosine Function
$\sin(x + \frac{\pi}{2}) = \cos(x)$

$\cos(x + \frac{\pi}{2}) = -\sin(x)$

$-\sin(x + \frac{\pi}{2}) = -\cos(x)$

$-\cos(x + \frac{\pi}{2}) = \sin(x)$

Whenever you add $\frac{\pi}{2}$ to the input you shift it to the left by Pi/2, so when you add Pi, you do that twice, so you effectively move from cos to -cos. So

$\sin(x + \pi) = -\sin(x)$
$\cos(x + \pi) = -\cos(x)$