Practice Pythagorean Trigonometric Identities in Math

Quick Recap

The fundamental identity ${\sin }^2\theta +{\cos }^2\theta =1$ and its derived forms: $1+{\tan }^2\theta ={\sec }^2\theta$ and $1+{\cot }^2\theta ={\csc }^2\theta$.

On the unit circle, the point $(\cos \theta ,\sin \theta )$ is always at distance 1 from the origin. By the Pythagorean theorem, $x^2+y^2=1$ becomes ${\cos }^2\theta +{\sin }^2\theta =1$. This single fact—that sine and cosine are tied to a circle—generates all three Pythagorean identities. Dividing through by ${\cos }^2\theta$ or ${\sin }^2\theta$ produces the other two forms.