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) | 0° | 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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