The **trigonometric ratios** are ratios of sides to one particular angle. These especially apply to right triangles and circles.

## BasicEdit

Here are the three basic trigonometric ratios you learn in geometry, using the Greek letter theta to represent an angle other than the right angle.

**Sine**Edit

- $ \sin{\theta\,}\, = \frac{opposite}{hypotenuse}\, $

**Cosine**Edit

- $ \cos{\theta\,}\, = \frac{adjacent}{hypotenuse}\, $

**Tangent**Edit

- $ \tan{\theta\,}\, = \frac{opposite}{adjacent}\, $

## AdvancedEdit

Here are three advanced trigonometric ratios you will learn by the time you get to calculus, again using theta.

**Cosecant**Edit

- $ \csc{\theta\,}\, = \frac{hypotenuse}{opposite}\, $

**Secant**Edit

- $ \sec{\theta\,}\, = \frac{hypotenuse}{adjacent}\, $

**Cotangent**Edit

- $ \cot{\theta\,}\, = \frac{adjacent}{opposite}\, $

## Degrees Or Radians?Edit

**Degrees**Edit

You use degrees when finding lengths and measurements of legs and angles in triangles.

- $ \sin{13}\, \approx\, 0.224951054343865... $
- $ \sin^{-1}{\frac{5}{6}\,}\, \approx\, 56.44269023807929... $

As is true for both triangles and circles, inverse trigonometric ratios will always give you the measure of the angle in question.

**Radians**Edit

You use radians when finding lengths and measurements of sectors and segments in circles. One radian is equal to a distance around a circle that is equivalent to the radius of that circle.

- $ \sin{13}\, \approx\, 0.420167036826641... $
- $ \sin^{-1}{\frac{5}{6}\,}\, \approx\, 0.985110783337746... $

Same numbers, different measurements, big difference! Be wary not to mix the two up!

See Trigonometric Identities for extra info.