## Trigonometry

Trigonometry is essential not just for achieving excellent grades in mathematics, but also in everyday life. Trigonometry begins with the two most fundamental functions, ratio and reciprocal. Trigonometric ratios are only computed for triangles with right angles.

The trigonometric concept is constructed on three basic foundations: sine, cosine, and tangent. Sin is one of the most important trigonometric ratios. Sin 30 degrees has a value of half (1/2).

## Trigonometric Ratios

Trigonometric ratios are used to compute the sides or angles of a triangle that cannot be determined from the triangle’s fundamental features. However, this only applies to triangles with right angles whose ratios of sides are stated as six trigonometric ratios.

Consider the triangle ABC in which C = 90 degrees. As the longest side, the side AB (opposite the right angle) is always the hypotenuse. Therefore, the side AB labelled c is the hypotenuse in this situation. Side CB is horizontal, but side CA is perpendicular.

Sinϴ= P/H

Cosϴ= B/H

Tanϴ= P/B

Sine of 30 Degrees Value

In order to define the sine function of an acute angle ϴ in a triangle ABC with right angles, it is necessary to name the sides according to the angles. Here are the three sides of the sin 30 triangles:

Triangle’s longest side is the hypotenuse or side C. It is directly opposite the triangle with a right angle and includes the unknown angle thetaϴ.

The side B is regarded as a base (adjacent) not only because the triangle rests on it, but also because it contains both angles, namely the 90-degree angle and the unknown angle thetaϴ.

Side A is the perpendicular (opposite) since it is the sole side next to the base that does not include the angleϴ.

According to the formula Sinϴ = Perpendicular /Hypotenuse, the sine function of an angle is the ratio of the perpendicular length to the hypotenuse length.

Derivation to Find the Sin 30 Value

To get the value of sin 30, we must thus know the length of each side of the triangle.

Consequently, let’s assume that AB=2a and that half of each side is a.

Sinϴ = Perpendicular Hypotenuse is the formula we will use to get the value of sin 30 degrees.

30 degree sin = BD/AB = a/2a = 12

Therefore, the value of Sin 30 degrees is 12(half) or 0.5.

Similar to how we calculated the value of sin 30 degrees, we can calculate the values of sin degrees 0°, 30°, 45°, 60°, 90°, 180°, 270°, and 360°.

## Solved Example

**Q.** In the triangle XYZ, right-angled at Y, Sise XY is equal to 10 centimetres, and the angle XZY is equal to 30 degrees. Determine how long each of the sides XZ is.

**A.**

Sin 30°= Perpendicular Hypotenuse

Sin 30°= XY / XZ

Putting Sin 30 value in

½ = XY/ XZ

½ = 10/ XZ

XZ = 20cm

Therefore, XZ = 20 cm.

Important formulas:

Important formulas: