Math Help - Trig identity for sqrt(2)/2?

1. Trig identity for sqrt(2)/2?

Does a trig identity exist for $\frac{\sqrt{2}}{2}$ ?

In other words, can $\frac{\sqrt{2}}{2}$ be expressed in terms of $\sin\theta, \cos\theta...$ etc. just as 1 can be set equal to $\sin^2\theta+\cos^2\theta$ ?

2. Draw yourself a right angled isosceles triangle with side lengths of 1, you will discover the following.

$\sin\left(\frac{\pi}{4}\right) = \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$

3. I mean a trig identity that works for ALL angles, just as $\sin^2\theta+\cos^2\theta$ always equals 1 for all $\theta$

4. Originally Posted by rainer
I mean a trig identity that works for ALL angles, just as $\sin^2\theta+\cos^2\theta$ always equals 1 for all $\theta$
the value of $\frac{\sqrt{2}}{2}$ is most always associated with the angle $\frac{\pi}{4}$ and some of its multiples ... not all angles, $\theta$ .