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 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. Read other details also provided by Edureify on Sin 30 degrees.
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:
- Sin 30:- Opposite side/Hypotenuse Side
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 concerning 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
Cosec 30 = 1/Sin 30
Cosec 30 = 1/(½)
Cosec 30 = 2
Why Sin 30 is equal to Sin 150
The value of sin 30 degrees and sin 150 degrees are equal.
Sin 30 = sin 150 = ½
Both are equal because the reference angle for 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, which forms a right triangle.
Since the angle of 150 degrees lies on the IInd quadrant, therefore the value of sin 150 is positive. The internal angle of a triangle is 180 – 150=30, which is the reference angle.
The value of sine in the other two quadrants, i.e. 3rd and 4th are negative.
In the same way,
Sin 0 = sin 180
Some Solved Questions on Sin 30
Question 1: If a right-angled triangle has a side opposite to an angle A, of 6cm and hypotenuse of 12cm. Then find the value of the angle.
Solution: Given, the Side opposite to angle A = 6cm
Hypotenuse = 12cm
By sin formula we know that;
Sin A = Opposite side to angle A/Hypotenuse
Sin A = 6/12 = ½
We know, Sin 30 = ½
So if we compare,
Sin A = Sin 30
A = 30
Hence, the required angle is 30 degrees.
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Question 2: If a right-angled triangle is having adjacent side equal to 10 cm and the measure of an angle is 45 degrees. Then find the value hypotenuse of the triangle.
Solution: Given adjacent side = 10cm
Tan 45 = Opposite side/Adjacent side
Tan 45 = opposite side/10
Since Tan 45 = 1
1 = Opposite side/10
Opposite side = 10 cm
Now, by sin formula, we know,
Sin A = Opposite side/Hypotenuse
Sin 45 = 10/Hypotenuse
Hypotenuse = 10/sin 45
Hypotenuse = 10/(1/√2)
Hypotenuse = 10√2
Frequently Asked Questions – FAQs
Question No 1:- What is the exact value of sine 30 degrees?
Ans:- The exact value of sin 30 degrees is 0.5.
Question No 2:- What is the value of sine 30 in the form of a fraction?
Ans:- The value of sin 30 in the form fraction is ½.
Question no 3:-What is sine 30 degrees in radian?
Ans:- Sine 30 degrees in radian is given by sin π/6.
Question No 4:- What is the formula for sine function?
Answer:- Sine of an angle, in a right-angled triangle, is equal to the ratio of opposite sides of the angle and hypotenuse.
Sine A = Opposite Side/Hypotenuse
Question No 5:- What is the value of cos 30 and tan 30?
Ans:- The value of cos 30 degrees is √3/2 and the value of tan 30 degrees is 1/√3.