CLEP Precalculus

CLEP Precalculus covers essential mathematical concepts and skills necessary for success in calculus and higher-level mathematics.

Advanced Topics

Trigonometric Functions and Applications

Measuring Angles and Cycles

Trigonometric functions, like sine, cosine, and tangent, relate angles to side lengths in right triangles and describe periodic phenomena.

The Six Functions

  • Sine (\( \sin \)), Cosine (\( \cos \)), Tangent (\( \tan \))
  • Cosecant (\( \csc \)), Secant (\( \sec \)), Cotangent (\( \cot \))

The Unit Circle

The unit circle helps visualize these functions for all angles, not just those in triangles. Every point on the unit circle has coordinates (\( \cos\theta, \sin\theta \)).

Applications

Trigonometric functions model waves, sound, and light. Engineers use them for designing everything from bridges to audio equipment.

Solving Problems

Use identities and inverse functions to solve equations and model cycles in nature and technology.

Key Formula

\[y = A \sin(Bx + C) + D\]

Examples

  • A sound wave can be modeled as \( y = 5\sin(2\pi t) \).

  • Finding the height of a tree using its shadow and angle of elevation.

In a Nutshell

Trigonometric functions describe cycles, angles, and waves, and are fundamental in science and engineering.

Key Terms

Unit Circle
A circle with radius 1, used to define trigonometric functions for all angles.
Amplitude
The height from the center line to the peak of a wave.