Trigonometric Ratios

Understanding Trigonometric Ratios

Trigonometric ratios are relationships between the sides and angles of a right-angled triangle. These ratios are essential for solving problems involving triangles and modeling periodic phenomena.

The primary trigonometric ratios are:

• Sine (sin): \$\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}} \\$
• Cosine (cos): \$\cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} \\$
• Tangent (tan): \$\tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} \\$

Special Angles

Certain angles have well-known trigonometric ratios that can be memorized for quick calculations. These include 30°, 45°, and 60°.

Angle	$\sin \theta$	$\cos \theta$	$\tan \theta$
30°	$\frac{1}{2}$	$\frac{\sqrt{3}}{2}$	$\frac{1}{\sqrt{3}}$
45°	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{2}}{2}$	1
60°	$\frac{\sqrt{3}}{2}$	$\frac{1}{2}$	$\sqrt{3}$

Using Trigonometric Tables

Trigonometric tables provide the values of sine, cosine, and tangent for various angles. These tables are useful for calculations without a calculator.