What function is y = cos(x +π) equal to

can you also explain the answer

thanks

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- Sep 23rd 2012, 07:14 AMubhuttoHelp with Cosine Function
What function is y = cos(x +

**π**) equal to

can you also explain the answer

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

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

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 $\displaystyle \theta$. The*x*-coordinate of this point is $\displaystyle \cos(\theta)$. To add $\displaystyle \pi$ 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 AMSworDRe: Help with Cosine Function
$\displaystyle \sin(x + \frac{\pi}{2}) = \cos(x)$

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

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

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

Whenever you add $\displaystyle \frac{\pi}{2}$ 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

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

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