Trigonometry

Study of triangles and trigonometric functions including sine, cosine, and tangent.

Basic Concepts

Trigonometric Ratios: Sine, Cosine, Tangent

The Big Three: Sine, Cosine, and Tangent

These trigonometric ratios help you find missing sides or angles in right triangles. They’re based on the relationships between the sides of a right triangle.

  • Sine (\(\sin\)): Ratio of the opposite side to the hypotenuse.
  • Cosine (\(\cos\)): Ratio of the adjacent side to the hypotenuse.
  • Tangent (\(\tan\)): Ratio of the opposite side to the adjacent side.

The Formulas

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \] \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \] \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]

If you remember SOH-CAH-TOA, you’re golden!

Why Use These Ratios?

They let you solve for unknown sides or angles, which is super useful in tons of real-life scenarios.

Examples

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

  • Calculating the length of a ramp needed to reach a certain height.

In a Nutshell

Sine, cosine, and tangent are ratios that relate the angles and sides in right triangles.

Key Terms

Hypotenuse
The longest side of a right triangle, opposite the right angle.
Adjacent
The side next to the angle in question.
Opposite
The side across from the angle in question.
Trigonometric Ratios: Sine, Cosine, Tangent - Trigonometry Content | Practice Hub