The triangle inequality for real numbers is $ |a+b| \le |a| + |b|$ in which […]

# Category: Trigonometry

## 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, $\theta$ […]

## The Pythagorean Theorem and the Unit Circle

This following diagram shows that $\displaystyle \sin^2 \theta + \cos^2 \theta = 1$, given $ […]

## Double Angle Formulas

In the Angle Addition Identities post it was shown that $ \displaystyle \sin(x+y) = \sin x \cos […]