Sin 30 Formula

In an equilateral triangle, the measure of each triangle is 60° and all the sides are equal.

Let’s assume all the side to be of 2 cm. After bisecting the angle, it would become 30° and length will be ½ (the side opposite angle which is 1), this way we get sin 30° as ½.

In a right angle triangle, one of the angles is 90°. To find the value of various trigonometric functions for different angles, we refer to the trigonometry table.

The trigonometry ratios can be defined in the trigonometry table to find the various values of angles like 300, 900 etc. These values play an important role in solving trigonometric equations.

Trigonometry Ratio Table for Sin 30 degree formula

Trigonometry Ratio Table
Angles (In Degrees) 30° 45° 60° 90°
Angles (In Radians) 0 π/6 π/4 π/3 π/2
sin 0 1/2 1/√2 √3/2 1
cos 1 √3/2 1/√2 1/2 0
tan 0 1/√3 1 √3 Not Defined
cot Not Defined √3 1 1/√3 0
csc Not Defined 2 √2 2/√3 1
sec 1 2/√3 √2 2 Not Defined

What is the Value of Sin 30°?

The value of sin 30 degrees can be found with the help of the above trigonometric table.

Sin 30° = 1/2

Solved Examples

Example 1: Find the value of sin 30° + 2 cos 60°.

Solution:
sin 30° + 2 cos 60°
= sin 30° + 2 cos (90° – 30°)
= sin 30° + 2 sin 30°
= 3 sin 30°
= 3(½)
= 3/2

Example 2: Simplify: 2 sin 30°/(1 – sin230°)

Solution:
2 sin 30°/(1 – sin230°)
= 2 (½)/[1 – (½)2] = 1/[1 – ¼] = 1/(¾)
= 4/3

Example 3: Find the value of 5 sin 30°/7 cos 60°.

Solution:
5 sin 30°/7 cos 60°
= 5 sin 30°/ 7 cos (90° – 30°)
= (5/7) (sin 30°/sin 30°)
= (5/7)(1)
= 5/7

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