what is the value of sin 30digree
Answers
The value of sin 30 degrees is 0.5. Sin 30 is also written as sin π/6, in radians. The trigonometric function also called as an angle function relates the angles of a triangle to the length of its sides.
Answer:
Sin 30 degrees
The value of sin 30 degrees is 0.5. Sin 30 is also written as sin π/6, in radians. The trigonometric function also called as an angle function relates the angles of a triangle to the length of its sides. Trigonometric functions are important, in the study of periodic phenomena like sound and light waves, average temperature variations and the position and velocity of harmonic oscillators and many other applications. The most familiar three trigonometric ratios are sine function, cosine function and tangent function.
Sine 30°=1/2
For angles less than a right angle, trigonometric functions are commonly defined as the ratio of two sides of a right triangle. The angles are calculated with respect to sin, cos and tan functions. Usually, the degrees are considered as 0°, 30°, 45°, 60°, 90°, 180°, 270° and 360°. Here, we will discuss the value for sin 30 degrees and how to derive the sin 30 value using other degrees or radians.
Sine 30 Degrees Value
The exact value of sin 30 degrees is ½. To define the sine function of an angle, start with a right-angled triangle ABC with the angle of interest and the sides of a triangle. The three sides of the triangle are given as follows:
The opposite side is the side opposite to the angle of interest.
The hypotenuse side is the side opposite the right angle and it is always the longest side of a right triangle
The adjacent side is the side adjacent to the angle of interest other than the right angle
The sine function of an angle is equal to the length of the opposite side divided by the length of the hypotenuse side and the formula is given by:
sinθ=opposite sidehypotenuse side
Sine Law: The sine law states that the sides of a triangle are proportional to the sine of the opposite angles.
asinA=bsinB=csinC
The sine rule is used in the following cases :
Case 1: Given two angles and one side (AAS and ASA)
Case 2: Given two sides and non included angle (SSA)
The other important sine values with respect to angle in a right-angled triangle are:
Sin 0 = 0
Sin 45 = 1/√2
Sin 60 = √3/2
Sin 90 = 1
Fact: The values sin 30 and cos 60 are equal.
Sin 30 = Cos 60 = ½
And
Cosec 30 = 1/Sin 30
Cosec 30 = 1/(½)
Cosec 30 = 2
Derivation to Find the Sin 30 value (Geometrically)
Let us now calculate the sin 30 value. Consider an equilateral triangle ABC. Since each angle in an equilateral triangle is 60°, therefore ∠A=∠B=∠C=60∘
sin 30 degrees
Draw the perpendicular line AD from A to the side BC (From figure)
Now ΔABD≅ΔACD
Therefore BD=DC and also
∠BAD=∠CAD
Now observe that the triangle ABD is a right triangle, right-angled at D with ∠BAD=30∘ and ∠ABD=60∘.
As you know, for finding the trigonometric ratios, we need to know the lengths of the sides of the triangle. So, let us suppose that AB=2a
BD=12BC=a
To find the sin 30-degree value, let’s use sin 30-degree formula and it is written as:
Sin 30° = opposite side/hypotenuse side
We know that, Sin 30° = BD/AB = a/2a = 1 / 2
Therefore, Sin 30 degree equals to the fractional value of 1/ 2.
Sin 30° = 1 / 2
Therefore, sin 30 value is 1/2
In the same way, we can derive other values of sin degrees like 0°, 30°, 45°, 60°, 90°,180°, 270° and 360°. Below is the trigonometry table, which defines all the values of sine along with other trigonometric ratios.