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

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## 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

Evaluate3(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

1. -1
2. 7
3. x = 23

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