Value of Sin 0

What is the Value of Sin 0

A little about Trigonometry and Trigonometric Ratios-

  • Trigonometric ratios in trigonometry are derived from the three sides of a right-angled triangle basically the hypotenuse, the base (adjacent), and the perpendicular (opposite).

  • According to the trigonometric ratio in maths, there are three basic or primary trigonometric ratios also known as trigonometric identities.

  • To be more specific, they are used in right-angled triangles, the triangles with one angle equal to 90 degrees


Sin 0 Value –

Sin 0⁰ Value = 0


Here are the primary trigonometric functions!

The primary trigonometric functions used are cosine, sine, and tangent. Sin 0 degrees value and other trigonometric ratios are used for common angles like 0°, 30°, 45°, 60°, 90° are used in trigonometric equations and calculations.


Name

Abbreviation

Relation

Sine

Sin

Sin (θ)= Opposite/Hypotenuse

Cosine

Cos

Cos (θ)= Adjacent/Hypotenuse

Tangent

Tan

Tan (θ)= Opposite/Adjacent



A Little Information About What a Right-Angled Triangle is?

Let us consider a right-angle triangle named ABC, with its three sides namely the opposite, adjacent, and the hypotenuse. In a right-angled triangle, we generally refer to the three sides according to their relation with the angle. The little box in the right corner of the triangle given below denotes the right angle which is equal to 90°. (image will be updated soon)


The 3 sides of a right-angled triangle are as follows-

  • The side opposite to the right angle is the longest side of the triangle which is known as the hypotenuse (H). 

  • The side that is opposite to the angle θ is known as the opposite (O). 

  • The side which lies next to the angle   is known as the Adjacent(A)

     Pythagoras theorem states that, 

In a right-angled triangle, 

(Opposite)2+(Adjacent)2= (Hypotenuse)2


As our angle of interest is Sin 0. So accordingly, the Sin function of an angle or Sin 0 degrees is equal to the ratio of the length of the opposite side to the length of the hypotenuse (longest side).


Sin 0 Formula - 

Sin 0 Value = Opposite side/Hypotenuse side


Derivation of Sin 0 Value – (image will be updated soon)


If we want to calculate the value of sin 0 degrees, we need to check the coordinates points on the x and y plane. Sin 0 signifies that the value of x coordinate is equal to 1 and the value of y coordinate is equal to 0, that is the coordinates (x, y) is (1, 0) which means that the value of When we place the values in sin ratio for θ=0° , substituting perpendicular side= 1 and hypotenuse = 0, 

We get,

Sin 0⁰ = 0/1

Or

Sin 0⁰ = 0

Now when we write the opposite of the value of Sin degrees, we get the values of cos degrees. 

As we know, Sin θ = 1/Cos θ

Therefore, we can now write the sin and cos values for different angles.

Sin 0° = Cos 90°=0

Sin 30° = Cos 60°

Sin 45° = Cos 45°

Sin 60° = Cos 30°=√3/2

Sin 90° = Cos 0°= 1


Similarly, we can write the value of Tan degrees, we get the values of cos and sin degrees. 

As we know, that the value of Tan θ = Sin θ / Cos θ

Therefore,

Tan 0°= Sin 0°/Cos 0°=0

Tan 30°=Sin 30°/Cos 30°= 1/√3

Tan 45°=Sin 45°/Cos 45°=1

Tan 60°=Sin 60°/Cos 60°=  √3

Tan 90°=Sin 90°/Cos 90°=Undefined


Table Showing the Different Values of Sin, Cos, and Tan for Different Angles.

Angles in Degrees

0⁰

30⁰

45⁰

60⁰

90⁰

Sin

0

1/2

1/√2

√3/2

1

Cos

1

√3/2

1/√2

1/2

0

Tan

0

1/√3

1

√ 3

Not defined

Cosec

Not defined

2

√ 2

2/√ 3

1

Sec

1

2/√3

√ 2

2

Not defined

Cot

Not defined

√3

1

1/√3

0


Table Showing Different Values of Sin, Cos, and Tan With Respect to Radians.

Angle

0⁰ 

   30⁰

  45⁰ 

  60⁰

  90⁰

  180⁰

  270⁰

  360⁰

Radian 

0

π/6

π/4

π/3

π/2

π

3π/2


Questions to be Solved -

Question 1) Evaluate the value of Sin 90⁰ + Cos 90⁰.

Solution) As we know that the value of Sin 90⁰ = 1

And the value of Cos 90⁰ = 0

Substituting the values of Sin 90⁰ and Cos 90⁰ ,

Therefore, Sin 90⁰ + Cos 90⁰ = 1 + 0

= 1


Question 2) What is the value of Sin 270⁰ + 2 Tan 45⁰.

Solution) As we know that the value of Sin 270⁰ = -1

And the value of Tan 45⁰ = 1

Substituting the values of Sin 270⁰ and Tan 45⁰ ,

Therefore, Sin 270⁰ + 2Tan 45⁰ = -1+2×1 = -1+2 = 1


Fun Facts –

1. Sin inverse is denoted as Sin-1 and it can also be written as arcsin or asine.

2. Hipparchus is known as the Father of Trigonometry. The value of arc and chord for a series of angles was discovered by him

3. Applications of Trigonometry you need to know-

  • Trigonometric ratios help us to find missing angles and missing sides of a triangle.

  • Trigonometry is widely used by the builders to measure the height and distance of the building from its viewpoint. 

  • It is also used by the students to solve the questions based on trigonometry.



Quiz Time-

Question 1) If x and y are considered as a complementary angle, then which of the following is correct?

a.   Tan x =Tan y

b.    Sin x=Sin y

c.    Cos x= Cos y

d.    Sec x= Cosec y

Answer) Option d


Question 2) What will be the value of sin 150°?

a.   1/5

b.    2

c.    1/2

d.    1

Answer) Option c

Sin 150°= Sin (90°+60°)

=Cos 60° {Since, (90+ϴ) = Cosϴ}

=1/2

FAQ (Frequently Asked Questions)

Question 1) What is the Value of Sin 0?

Answer) In Mathematics, the value of sin 0 degree is always equal to 0.

Question 2) When Sin is 0?

Answer) Sin(x) is a periodic trigonometric function that oscillates at regular intervals. Sin function crosses the x-axis, that is the value of sin function is zero when the value of x = 0, π , 2π and the function continues to cross the x-axis at every multiple of π.

Question 3) What Does Sin 0 Mean and What is the Value of Sin 0?

Answer) Basically, sin(x) can be defined as (opposite side of a triangle/ adjacent side of a triangle). If the value of the angle between the hypotenuse and the adjacent side is equal to zero, then there is no opposite side, which means the length of the opposite is zero. Hence, the ratio is equal to zero.