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

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° +  cosec³ 30° – 3 tan 45°

Problem 3.  Solve: sin² 60°+ cos² (3x – 9)  = 1

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