Trigonometry Formulas Review

Comprehensive vocabulary flashcards covering basic trigonometric identities, double angle formulas, power reduction identities, and sum-to-product transformations derived from the lecture notes.

Pythagorean Identity (Sine and Cosine)

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

Pythagorean Identity (Tangent and Secant)

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

Pythagorean Identity (Cotangent and Cosecant)

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

Cosecant Reciprocal Identity

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

Secant Reciprocal Identity

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

Cotangent Identities

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

Tangent Quotient Identity

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

Sine Double Angle Formula

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

Sine Identity (Half-Angle Form)

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

Cosine Double Angle Formula (Basic)

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

Sine and Cosine Square Difference Identity

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

Cosine Power Reduction (Double Angle)

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

Cosine Power Reduction (Single Angle)

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

Sine Power Reduction (Double Angle)

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

Sine Power Reduction (Single Angle)

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

Tangent Sum and Difference Formula

$$\tan(A \pm B) = \frac{\tan(A) \pm \tan(B)}{1 \mp \tan(A)\tan(B)}$$

Sine Sum and Difference Formula

$$\sin(A \pm B) = \sin(A)\cos(B) \pm \cos(A)\sin(B)$$

Cosine Sum and Difference Formula

$$\cos(A \pm B) = \cos(A)\cos(B) \mp \sin(A)\sin(B)$$

Tangent Double Angle Formula

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

Sine Sum-to-Product Formula

$$\sin(C) + \sin(D) = 2\sin(\frac{C+D}{2})\cos(\frac{C-D}{2})$$

Sine Difference-to-Product Formula

$$\sin(C) - \sin(D) = 2\sin(\frac{C-D}{2})\cos(\frac{C+D}{2})$$

Cosine Sum-to-Product Formula

$$\cos(C) + \cos(D) = 2\cos(\frac{C+D}{2})\cos(\frac{C-D}{2})$$

Cosine Difference-to-Product Formula

$$\cos(C) - \cos(D) = -2\sin(\frac{C+D}{2})\sin(\frac{C-D}{2})$$