Trigonometric Ratios for 0°, 30°, 45°, 60° angles

What are Trigonometric Ratios?

✓ Ratios of the sides in a right triangle with respect to some acute angles are called trigonometry ratios for specific angles.

✓ The angles 0°, 30°, 45°, 60°, 90° are useful angles in trigonometry.

✓ Trigonometric ratios of angles help in simplifying problems.

Values of Trigonometric Ratios for 0°, 30°, 45°, 60° angles

Example 1:

Find: Cosec²30° Sin²30° – Sec²60°

Putting the values of Cosec 30˚ = 2, sin 30° = 1/2, sec 60° = 2

We get,

= (2)² x (1/2)² – (2)²

= (4 x ¼) – 4

= 1 – 4 = -3

Example 2:

Evaluate: 3(cos 30°)² + (sin 30°)²

We know, cos 30° = √3/2 and sin 30° = 1/2

3(√3/2)²+ (1/2)²

3 x 3 /4 + 1/4

= 9/4 + 1/4

= 10/4

= 5/2

Checkpoint

Problem 1. 2 sin 30° + 2cos 60° – 3 tan 45°

Problem 2. sec²45° + cosec³30° – 3 tan 45°

Problem 3. Solve: sin²60°+ cos²(3x – 9) = 1

Answer Key

-1
7
x = 23

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