Trigonometric functions

Definition

Trigonometric functions are mathematical functions that relate the angles of a triangle to the lengths of its sides. They are fundamental in studying periodic phenomena and are defined using the unit circle.

5 Must Know Facts For Your Next Test

1. The six main trigonometric functions are sine ($\sin$), cosine ($\cos$), tangent ($\tan$), cosecant ($\csc$), secant ($\sec$), and cotangent ($\cot$).
2. Sine and cosine functions are periodic with a period of $2\pi$, while tangent and cotangent have a period of $\pi$.
3. The values of trigonometric functions can be positive or negative depending on the quadrant of the angle in the unit circle.
4. The Pythagorean identity states that $\sin^2(\theta) + \cos^2(\theta) = 1$ for any angle $\theta$.
5. Tangent is defined as the ratio $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$, while cotangent, secant, and cosecant are its reciprocals.

Review Questions

• What is the period of the sine function?
• How is tangent function related to sine and cosine?
• State the Pythagorean identity involving sine and cosine.

Related terms

Unit Circle: A circle with radius 1 centered at the origin (0,0) in a coordinate plane, used to define trigonometric functions.

Sine Function: A trigonometric function represented by $ \text{sin}(x)$, which gives the y-coordinate of a point on the unit circle.

Cosine Function: A trigonometric function represented by $ \text{cos}(x)$, which gives the x-coordinate of a point on the unit circle.