## Proof of the Triangle Inequality for Real Numbers

The triangle inequality for real numbers is $|a+b| \le |a| + |b|$ in which $a$ is a variable for a real number, and $b$ is a variable for a real number. Proof:…

## Do the angle addition identities only work for positive angles?

The Angle Addition Identities were derived using $\sin\theta \equiv \frac{opp}{hyp}$ and $\cos\theta \equiv \frac{adj}{hyp}$. In addition, $\theta$ was constrained to the interval of $[0, \frac{\pi}{2})$. The question addressed in this post is, do the Angle…

This following diagram shows that $\displaystyle \sin^2 \theta + \cos^2 \theta = 1$, given $\displaystyle \cos \theta \equiv \frac{adj}{hyp}$ and $\displaystyle \sin \theta \equiv \frac{opp}{hyp}$ and the Pythagorean theorem. Here, $opp$,…
In the Angle Addition Identities post it was shown that $\displaystyle \sin(x+y) = \sin x \cos y + \sin y \cos x$ and \$ \displaystyle \cos(x+y) = \cos x \cos y – \sin…