Trigonometric Identities

Vocabulary flashcards covering core trigonometric identities, exact values, identity rearrangements, and proof strategies.

Exact value of $\sin(60)$

The exact value of $\sin(60)$, which equals $\frac{\sqrt{3}}{2}$.

Exact value of $\cos(60)$

The exact value of $\cos(60)$, which equals $\frac{1}{2}$.

Exact value of $\tan(60)$

The exact value of $\tan(60)$, which is equal to $\sqrt{3}$ and obtained by dividing $\sin(60)$ by $\cos(60)$.

Identity Sign

A mathematical symbol used in place of an equals sign to indicate that a relation holds true for any chosen angle $\theta$.

Tangent Quotient Identity

The identity stating that $\tan(\theta) \equiv \frac{\sin(\theta)}{\cos(\theta)}$ for any angle $\theta$.

Reciprocal Tangent Identity

The identity derived by taking the reciprocal of both sides of the tangent identity, giving $\frac{1}{\tan(\theta)} \equiv \frac{\cos(\theta)}{\sin(\theta)}$.

Pythagorean Trigonometric Identity

The identity stating that $\sin^2(\theta) + \cos^2(\theta) \equiv 1$ for any angle $\theta$.

Rearrangement for $\sin^2(\theta)$

An alternate form of the Pythagorean identity obtained by subtracting $\cos^2(\theta)$ from both sides, written as $\sin^2(\theta) \equiv 1 - \cos^2(\theta)$.

Rearrangement for $\cos^2(\theta)$

An alternate form of the Pythagorean identity obtained by subtracting $\sin^2(\theta)$ from both sides, written as $\cos^2(\theta) \equiv 1 - \sin^2(\theta)$.

Trigonometric Identity Proof Method

The standard proof strategy of starting strictly with the left hand side (LHS), applying algebraic and trigonometric substitutions step-by-step, and arriving at the right hand side (RHS).