[Maths Class Notes] on Sin 30 Degrees Pdf for Exam

Trigonometry is not only important to score high marks in mathematics but also in day-to-day life.  Trigonometry starts with the most important functions of ratio and reciprocal. Trigonometric ratios are calculated only for right angled triangles

Sine, cosine and tangent are the three main pillars on which the whole concept of trigonometry rests. Sin is one of those important trigonometric ratios. The value of sin 30 degrees is half (½).  Just to recapitulate the sides of a triangle, let’s go through the following definitions once again since this will help the students to understand the sides and their ratios in relevance to trigonometry.

 

 

 

Trigonometric Ratios

Trigonometric ratios are used to calculate the unknown sides or angles of a triangle that can not be calculated from the simple properties of triangles. However this is only applicable for right angled triangles where the ratios of sides are expressed in the form of six trigonometric ratios. They are Sin, Cos, Tan, Cosec, Sec, and Cot which are actually the ratio of the sides of a right-angled triangle. 

 

Let us consider a triangle ∆ABC, in which ∠C = 90°. The side AB (opposite to the right angle) is always the hypotenuse because it is the longest side. So, the side AB named as c is the hypotenuse in this particular case. Side CB is base and side CA is perpendicular.

 

 

 

 

Reciprocals:

1. The reciprocal or inverse of Sin is Cosec. That is,

If Sinϴ = Perpendicular / Hypotenuse then Cosec ϴ = Hypotenuse /Perpendicular

2. The reciprocal or inverse of Cos is Sec. That is,

If Cosϴ = Base / Hypotenuse then Sec ϴ = Hypotenuse/ Base

3. The reciprocal or inverse of Tan is Cot. That is,

If Cosϴ = Base / Hypotenuse then Sec ϴ = Hypotenuse /Base

Usually, the trigonometric ratios are calculated for all the angles less than 90 degrees but given below are the basic ones. 

Basic degrees: 0°, 30°, 45°, 60°, 90°, 180°, 270° and 360°. 

Given below is a for the values of all trigonometric ratios of the standard trigonometric angles, that is, 0°, 30°, 45°, 60°, and 90°. In this chapter, we are going to discuss the value of sin 30 degrees. 

Trigonometric Values

 

 

Sine of 30 Degrees Value

In order to express the sine function of an acute angle ϴ of a right-angled triangle ABC, it is important to name the sides based on the angles. The three sides of sin 30 triangle are given as follows:

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• The longest side of the triangle, that is, the side C is the hypotenuse. It is right opposite to the right-angled triangle and also contains the unknown angle theta.

• The side B is considered as a base (adjacent) not only because triangle rests on it but also because it has both the angles, that is, 90 degree and unknown angle theta ϴ 

• Side A is the perpendicular (opposite) as it is the only side that does not contain the angle ϴ and is adjacent to the base.

As we know, The sine function of an angle is equal to the ratio of the length of perpendicular to the length of Hypotenuse and the formula is given by,

Sinϴ = Perpendicular /Hypotenuse.

Sine Law:

The sine law affirms that “the sides of a triangle are proportional to the sine of the opposite angles.”

Let us take a normal triangle ABC, 

 

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Now, according to the rule, 

a/Sin A = b/Sin B= c/Sin C = d

We use sine law when:

1. Two angles and one side of a triangle given.

2. Two sides and one included angle are given.
   

Derivation to Find the Sin 30 Value

Let us consider an equilateral triangle ABC having all the angles as 60 degrees. Now, the question is what is the value of sin 30  and what is the opposite of sin ?

 

Hence to find the answer of sin 30 value  we need to know the length of all the sides of the triangle.

 

So, let us suppose that AB=2a, such that half of each side is a.

 

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To find the value of sin 30 degree, we will use the following formula,

 

Sinϴ = Perpendicular Hypotenuse.

 

           Sin 30° = BD/AB =  a/2a = 12

 

Thus, the value of Sin 30 degrees is equal to 12(half) or 0.5.

 

Just like the way we derived the value of sin 30 degrees, we can derive the value of sin degrees like 0°, 30°, 45°, 60°, 90°,180°, 270° and 360°. 

 

has arranged the chapter of trigonometry with utmost care with lots of examples and derivations done by subject teachers in an easy understandable way. They have given special focus on each function separately like here for sin30 degrees.

 

Solved Examples

Example 1: In triangle XYZ, right-angled at Y, XY = 10 cm and angle XZY = 30°. Find the length of the side XZ.

Solution:

To find the length of the side XZ, we use the formula of the sine function, which is ,

 

Sin 30°= Perpendicular Hypotenuse

 

Sin 30°= XY / XZ

 

On substituting the value of sin 30

 

½ = XY/ XZ

 

½ = 10/ XZ

 

XZ = 20cm 

 

Therefore, the length of the side, XZ = 20 cm.

 

Example 2: How do I find the value of sin(-30)?

Solution: 

Sin (-30) = – Sin (30)

 

Sin 30 = ½

 

Therefore sin (-30) = – ½ .