Sin 30 degrees | Top Q&A

The value of the 30 degree sine is 0.5. Sin 30 is also written as sin π / 6, in radians. The trigonometric function, also known as the angle function, relates the angles of a triangle to the lengths of its sides. Trigonometric functions are important, in the study of periodic phenomena such as sound and light waves, average temperature changes, position and velocity of harmonic oscillations, and many other applications. The three most familiar trigonometric ratios are the sine function, the cosine function, and the tangent function. Sine 30° = 1/2 For an angle less than a right angle, the trigonometric function is usually defined as the ratio of the two sides of a right triangle. The angles are calculated using the sine, cosine and tan functions. Typically, the degrees are considered 0°, 30°, 45°, 60°, 90°, 180°, 270°, and 360°. Here, we will discuss the value of sine 30 degrees and how to calculate the value of sine 30 using degrees or other radians.

Sine value 30 degrees

Contents

The exact value of a 30 degree sine is ½. To determine the sine function of an angle, start with a right 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 face opposite the angle of interest.
  • The hypotenuse is the side opposite the right angle and it is always the longest side of a right triangle
  • Adjacent edge is the side adjacent to the preferred angle 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 and the formula is given by: [latex]sin theta = frac {opposite ~ side} {hypogonal ~ side}[/latex]Law of sine: The law of sine states that the sides of a triangle are proportional to the sine of the opposite angles. [latex]frac {a} {sin A} = frac {b} {sin B} = frac {c} {sin C}[/latex]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 an excluding angle (SSA) Other significant sine values ​​for with the angle in the triangle square whose angle is: Sin 0 = 0Sin 45 = 1 / 2Sin 60 = 3 / 2Sin 90 = 1Reality: The values ​​of sin 30 and cos 60 are equal. Sin 30 = Cos 60 = ½AndCosec 30 = 1 / Sin 30Cosec 30 = 1 / (½) Cosec 30 = 2

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Derivative to find Sin 30 value (Geometrically)

Now let’s calculate the sine value 30. Consider the equilateral triangle ABC. Since each angle in an equilateral triangle is 60°, so [latex]angle A = angle B = angle C = 60 ^ {circle}[/latex]Draw a line perpendicular to AD from A to side BC (From the figure) Now [latex]Delta ABDcong Delta ACD[/latex]Hence BD = DC and also [latex]angle BAD = angle CAD[/latex]Now observe that triangle ABD is a right-angled, right-angled triangle at D with [latex]angle BAD = 30 ^ {circle}[/latex] and [latex]angle ABD = 60 ^ {circle}[/latex].Read more: Factor 80 | Top Q&A you know, to find trigonometric ratios, we need to know the lengths of the sides of the triangle. So let’s say AB = 2a [latex]BD = fraction {1} {2} BC = a[/latex]To find the 30 degree sine value, use the 30 degree sine formula and it is written as: Sin 30° = opposite side / hypotenuse We know that, Sin 30° = BD / AB = a / 2a = 1/2 Hence, The 30 degree sine is equal to the fractional value of 1/2.Sin 30° = 1/2 Hence, the value of sine 30 is 1/2 In the same way we can deduce other values ​​of sine degrees like 0°, 30°, 45°, 60°, 90 °, 180°, 270° and 360°. Below is a trigonometric table, identifying all the values ​​of sine along with other trigonometric ratios. Related Links Sin 0 Degree Trigonometric Formula Inverse of the Law of Cosine of the Sines . Formula

Why is Sin 30 equal to Sin 150

The values ​​of sine 30 degrees and sine 150 degrees are equal. Sin 30 = sin 150 = ½Both are equal because the reference angle 150 is equal to 30 for the triangle formed in the unit circle. The reference angle is formed when the perpendicular is dropped from the unit circle to the x-axis, forming a right triangle Since the 150 degree angle lies on the second quadrant, the value of sin 150 is the interior angle of the topqa. info of the triangle is 180 – 150 = 30, which is the reference angle. The value of the sine in the other two quadrants i.e. 3rd and 4th is negative. Similarly, Sin 0 = sin 180

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Trigonometric table

Table of trigonometric ratios Angle (In degrees) 0334390000 180 270 360 Angle (In Radian) 0 / 6 / 4 / 3 / 2 3π / 2 2π sin 0 1/2 1 / 2 3 / 2 1 0 −1 0 cos 1 √3 / 2 1 / 2 1/2 0 −1 0 1 tan 0 1 / 3 1 √3 Unknown 0 Unknown 0 cot Unknown 3 1 1 / 3 0 Unknown 0 Unknown cosec Unknown 2 √2 2 / 3 1 Unknown −1 Unknown seconds 1 2 / 3 √2 2 Unknown −1 Unknown 1

Solved examples

Question 1: In an isosceles right triangle ABC at B, AB = 5 cm and angle ACB = 30°. Determine the length of side AC.sine 30 degrees 1Solution:To find the side length AC, we consider the sine function, and the formula is given by Sin 30° = Opposite side / Implicit sideSin 30° = AB / AC Take the value sine 30 and the value AB, [latex]frac {1} {2} = frac {5} {AC}[/latex]Therefore, the length of the hypotenuse, AC = 10 cm.Question 2: If a right triangle has side to side A is 6cm and hypotenuse is 12cm. Then find the value of the angle.Solution: Given, Side opposite angle A = 6cmRead more: Difference between | Descriptive and Comparative Analysis Hypotenuse = 12cm According to the sine formula, we know that; Sin A = Side opposite angle A / HypotenuseSin A = 6/12 = ½ We know, Sin 30 = ½ So if we compare, Sin A = Sin 30A = 30 So the angle needed is 30 degree.Question 3: If an isosceles right triangle has side length 10 cm and angle measure 45 degrees. Then find the hypotenuse of the triangle.Solution: Given adjacency = 10cm We know, Ton 45 = Opposite side / Adjacent side Tan 45 = opposite side / 10 Because, Ton 45 = 1 So 1 = Opposite side / 10 Opposite side = 10 cm Now, according to sine formula, we know, Sin A = Opposite / HypotenuseSo, Sin 45 = 10 / HypotenuseHypotenuse = 10 / sin 45Hypotenuse = 10 / (1 / √2) Hypotenuse = 10√2Continue to visit BYJU’S for more information information on trigonometric ratios and related articles, and watch videos to clear doubts.Read more: How do cactus taste

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