Thread: Trig identity for sqrt(2)/2?

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

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

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

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

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

Originally Posted by rainer

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

the value of $\displaystyle \frac{\sqrt{2}}{2}$ is most always associated with the angle $\displaystyle \frac{\pi}{4}$ and some of its multiples ... not all angles, $\displaystyle \theta$ .