# How do you find the cos of theta if #abs(sintheta)=1#?

##### 1 Answer

May 25, 2016

#### Explanation:

No matter what the value of

#cos^2 theta + sin^2 theta = 1#

Considering

#abs(sin theta) = 1# implies#sin theta = +-1# , which implies#sin^2 theta = 1#

So:

#cos^2 theta = 1 - sin^2 theta = 1-1 = 0#

So:

#cos theta = 0#

**Complex footnote**

The same does not hold if

For any value of

#cos z = (e^(iz)+e^(-iz))/2#

#sin z = (e^(iz)-e^(-iz))/(2i)#

For example:

If

#sin(theta) = i# , so#abs(sin(i)) = 1#

#cos(theta) = sqrt(2)#