Trigonometric Values
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The Basics
The three primary trigonometric functions are sine, cosine, and tangent.
- Sine (sin): The ratio of the length of the side opposite the angle to the length of the hypotenuse. $$ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} $$
- Cosine (cos): The ratio of the length of the adjacent side to the length of the hypotenuse. $$ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} $$
- Tangent (tan): The ratio of the length of the opposite side to the length of the adjacent side. $$ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} $$
Common Angles
Here is a table of trigonometric values for common angles:
| $$ 0 $$ | $$ \frac{\pi}{6} $$ | $$ \frac{\pi}{4} $$ | $$ \frac{\pi}{3} $$ | $$ \frac{\pi}{2} $$ | |
|---|---|---|---|---|---|
| $$ \sin $$ | 0 | $$ \frac{1}{2} $$ | $$ \frac{\sqrt{2}}{2} $$ | $$ \frac{\sqrt{3}}{2} $$ | 1 |
| $$ \cos $$ | 1 | $$ \frac{\sqrt{3}}{2} $$ | $$ \frac{\sqrt{2}}{2} $$ | $$ \frac{1}{2} $$ | 0 |
| $$ \tan $$ | 0 | $$ \frac{1}{\sqrt{3}} $$ | 1 | $$ \sqrt{3} $$ | Undefined |
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