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.

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,

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).

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.

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,

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

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.