IndietroEssential Trigonometric Values and Identities
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Trigonometric Functions: Key Angles and Values
Common Angles in Degrees and Radians
Understanding the values of trigonometric functions at standard angles is fundamental in precalculus and trigonometry. The following table summarizes the sine, cosine, and tangent values for commonly used angles, along with their degree and radian measures.
Angle (Degrees) | Angle (Radians) | sin(θ) | cos(θ) | tan(θ) |
|---|---|---|---|---|
0° | $0$ | $0$ | $1$ | $0$ |
30° | ||||
45° | $1$ | |||
60° | ||||
90° | $1$ | $0$ | undefined | |
120° | ||||
135° | ||||
150° | ||||
180° | $0$ | $0$ | ||
270° | $0$ | undefined | ||
360° | $0$ | $1$ | $0$ |
Reciprocal Trigonometric Identities
Each basic trigonometric function has a reciprocal function. These identities are essential for simplifying expressions and solving equations.
Cosecant:
Secant:
Cotangent:
Memory Patterns for Sine and Cosine
To quickly recall the values of sine and cosine for the key angles in the first quadrant, observe the following patterns:
Sine values (0° to 90°):
Cosine values (0° to 90°):
These patterns help in memorizing the trigonometric values efficiently.
Example: Evaluating Trigonometric Functions
Example 1: Find and .
From the table: ,
Example 2: Find .
From the table:
Example 3: Find .
First,
So,
