Trigonometry Function Identities

This set of flashcards covers essential trigonometry identities including quotient, reciprocal, Pythagorean, double angle, and half angle identities.

Quotient Identity for tan(θ)

$$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$$

Quotient Identity for cot(θ)

$$\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}$$

Reciprocal Identity for sin(θ)

$$\sin(\theta) = \frac{1}{\csc(\theta)}$$

Reciprocal Identity for csc(θ)

$$\csc(\theta) = \frac{1}{\sin(\theta)}$$

Reciprocal Identity for cos(θ)

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

Reciprocal Identity for sec(θ)

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

Reciprocal Identity for tan(θ)

$$\tan(\theta) = \frac{1}{\cot(\theta)}$$

Reciprocal Identity for cot(θ)

$$\cot(\theta) = \frac{1}{\tan(\theta)}$$

Pythagorean Identity (sin and cos)

$$\sin^2(\theta) + \cos^2(\theta) = 1$$

Pythagorean Identity (sec and tan)

$$\sec^2(\theta) - \tan^2(\theta) = 1$$

Pythagorean Identity (csc and cot)

$$\csc^2(\theta) - \cot^2(\theta) = 1$$

Double Angle Identity for sin(2θ)

$$\sin(2\theta) = 2\sin(\theta)\cos(\theta)$$

Double Angle Identity for cos(2θ) (Form 1)

$$\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta)$$

Double Angle Identity for cos(2θ) (Form 2)

$$\cos(2\theta) = 2\cos^2(\theta) - 1$$

Double Angle Identity for cos(2θ) (Form 3)

$$\cos(2\theta) = 1 - 2\sin^2(\theta)$$

Double Angle Identity for tan(2θ)

$$\tan(2\theta) = \frac{2\tan(\theta)}{1 - \tan^2(\theta)}$$

Half Angle Identity for sin²(θ)

$$\sin^2(\theta) = \frac{1 - \cos(2\theta)}{2}$$

Half Angle Identity for cos²(θ)

$$\cos^2(\theta) = \frac{1 + \cos(2\theta)}{2}$$

Half Angle Identity for tan²(θ)

$$\tan^2(\theta) = \frac{1 - \cos(2\theta)}{1 + \cos(2\theta)}$$