Sin 30 Formula

Sin 30 Formula: Sin 30 degrees is equal to cos 60 degrees. The value of sin 30 degrees is 1/2.

What is the formula for sin 30?

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 of the side will be ½ (the side opposite to the angle 60 degrees which equal to 1), this way we get sine 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.

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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