In trigonometry, there are three major or primary ratios, Sine, Cosine and Tangent, which are used to find the angles and length of the right-angled triangle. Lets discuss about Sine ratio in detail in this blog.

**What is sine or sin?**

**What is sine or sin?**

**Sine function** defines a relation between the angle(formed between the hypotenuse and adjacent side) and the opposite side to the angle and hypotenuse. Or you can say, the Sine of angle theta is equal to the ratio of perpendicular and hypotenuse of a right-angled triangle. The sine function plays a crucial role in geometry. According to the property of a right-angled triangle, when an angle measures 90°, the sum of the remaining two angles equals the third angle. The major angles that can be noted are 0°, 30°, 45°, 60°, and 90°.

**Value of sin 60°**

**Value of sin 60°**

Sin defines the ratio between the perpendicular of the right-angled triangle to that of the hypotenuse of the right-angled triangle. In decimal form, its value is 0.8660254.

Sin θ = opposite side /hypotenuse = perpendicular/hypotenuse

**Sin 60° using Unit Circle**

**Sin 60° using Unit Circle**

Follow the steps given below to find the value of Sin 60° using the Unit Circle.

- Using the positive x-axis, rotate the ‘r’ in an anticlockwise direction so that a 60° angle is formed.

- The coordinate y which is of the Sin 60° is then equal to the value of 0.866 and the intersection point of the unit circle and r. (0.5,0.866)

- This gives us the Sin 60°= 0.866.

**Degrees and Radian**

**Degrees and Radian**There are two ways to measure any angle: degree and radian. While radians are depicted using a ‘π’ symbol, degrees are represented with the symbol ‘°’. Notably, a circle is equivalent to 360° or 2 radians, as one radian is equivalent to 180°. Furthermore, degrees can be further categorized into minutes and seconds.

**Trigonometric Functions Related to Sin 60°**

Sin 60° will always yield a positive value as it lies in the first quadrant.

Some of the formulas represented by Sin 60° are:

1. ± √ (sec² (60°) – 1)/sec 60°

2. ± √ (1-cos² (60°))

3. ± 1/√ (1 + cot² (60°))

4. 1/cosec 60°

5. ± tan 60°/√ (1 + tan² (60°))

6. sin (180° – 60°) = sin 120°

7. cos (90° – 60°) = cos 30°

8. -sin (180° + 60°) = -sin 240°

9. -cos (90° + 60°) = -cos 150°

**Things to Remember**

Sin function can be defined as the ratio in a right-angled triangle between its two sides that is perpendicular to that of the hypotenuse.

- In fractional form, the value of sin 60°= √3/2
- Sin 60°, when denoted in terms of a radian, is π/3
- The two ways by which the value of the sin 60° can be predicted are by either using the trigonometric functions or by using the unit circle.
- A radian is equal to 180° which is denoted a semi-circle while 2π depicts a full circle.