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