## 17Calculus Precalculus - Trigonometry Summary

##### 17Calculus

Trig Summary

This page contains a summary, without explanation, of the trig information you need for calculus. For full discussion, go to the trigonometry page.

Unit Circle

The Unit Circle [source: wikipedia]

Set 1 - Basic Identities

$$\displaystyle{ \sin(t) = \frac{\text{opposite}}{\text{hypotenuse}} }$$

$$\displaystyle{ \cos(t) = \frac{\text{adjacent}}{\text{hypotenuse}} }$$

$$\displaystyle{ \tan(t) = \frac{\sin(t)}{\cos(t)} }$$

$$\displaystyle{ \cot(t) = \frac{\cos(t)}{\sin(t)} }$$

$$\displaystyle{ \sec(t) = \frac{1}{\cos(t)} }$$

$$\displaystyle{ \csc(t) = \frac{1}{\sin(t)} }$$

Set 2 - Squared Identities

$$\sin^2t + \cos^2t = 1$$

$$1 + \tan^2t = \sec^2t$$

$$1 + \cot^2t = \csc^2t$$

Set 3 - Double-Angle Formulas

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

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

Set 4 - Half-Angle Formulas

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

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

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