Trig ID Practice 2025

A Pythagorean identity is a fundamental relation between the trigonometric functions sine, cosine, and tangent, derived from the Pythagorean theorem. The most common identities are: 1. $$\tan^2x + 1 = \frac{1}{\text{cos}^2x}$$ 2. $$1 + \tan^2x = \text{sec}^2x$$ 3. $$1 + \text{cot}^2x = \text{csc}^2x$$ .

The identity $$\text{csc}^2x + 1 = \text{cot}^2x$$ is NOT a Pythagorean identity.

$$\text{sec}(\theta) = \frac{1}{\text{cos}(\theta)}$$ .

The relationship is given by the identity: $$\text{sec}^2x - 1 = \tan^2x$$ .

$$\text{csc}(\frac{\text{π}}{2} - \theta) = \text{sec}(\theta)$$ .

$$\tan^2x + 1 = \text{sec}^2x$$ .

$$\text{cot}^2x + 1 = \text{csc}^2x$$ .

The reciprocal identity for sine is: $$\text{csc}(\theta) = \frac{1}{\text{sin}(\theta)}$$ .

The reciprocal identity for cosine is: $$\text{sec}(\theta) = \frac{1}{\text{cos}(\theta)}$$ .

The reciprocal identity for tangent is: $$\text{cot}(\theta) = \frac{1}{\text{tan}(\theta)}$$ .