In trigonometry, there are three major or primary function, Sine, Cosine and Tangent, which are used to find the angles and length of the right-angled triangle. Before discussing Sin 0, let us know about Sine function.

Sine function defines a relation between the angle and perpendicular side and hypotenuse side. Or you can sin theta (the angle formed between the hypotenuse and adjacent side) is equal to the ratio of perpendicular and hypotenuse of a right-angled triangle.

Let us discuss more of the trigonometric sine functions here in this article.

Sine Definition In Terms of Sin 0

As we have already discussed, the sin of angle theta is a ratio of the length of the opposite side, perpendicular and hypotenuse of the right-angled triangle.

Sin \(\theta\) = \(\frac{Opposite Side}{Hypotenuse}\)

= \(\frac{Perpendicular}{Hypotenuse}\)

Now if we want to calculate sin 0 degrees value, we have to check the coordinates point on x and y plane. Sin 0 signifies that the value of x coordinate is 1 and the value of y coordinate is 0,i.e. (x,y) is (1,0). That means the value of the opposite side or perpendicular is zero and the value of hypotenuse is 1. So if we place the values in sin ratio for \(\theta\)=0⁰ , perpendicular side= 1 and hypotenuse as 0, then we get,

Sin 0⁰ =0/1

Or

Sin 0⁰ = 0

From the above equation, we have yield sin 0 degrees value. Now let us write other sin degrees or radians values for one full revolution, in a table.

If we write opposite of the value of Sin degrees, we get the values of cos degrees. Because, Sin \(\theta\)=1/Cos\(\theta\)

Therefore we can write,

Sin 0⁰= Cos 90⁰=0

Sin 30⁰=Cos 60⁰=½

Sin 45⁰=Cos 45⁰ = \(1/\sqrt{2}\)

Sin 60⁰=Cos 30⁰=\(\sqrt{3}/2\)

Sin 90⁰=Cos 0⁰=1

In the same way, we can write the values for Tan degrees.

Tan \(\theta\)=Sin\(\theta\)/Cos\(\theta\)

Therefore,

Tan 0⁰=Sin 0⁰/Cos 0⁰=0

Tan 30⁰=Sin 30⁰/Cos 30⁰=\(\sqrt{3}\)/2

Tan 45⁰=Sin 45⁰/Cos 45⁰=1

Tan 60⁰=Sin 60⁰/Cos 60⁰=\(\sqrt{3}\)

Tan 90⁰=Sin 90⁰/Cos 90⁰=Undefined

We learned about sin theta 0 degrees value along with other degree values here, this far. Also, derived the value for cos degree and tan degrees with respect sin degrees. In the same way, we can find other trigonometric ratios like sec, cosec and cot.

Based on these values, we can draw the trigonometry table,

Example: Find the value of Sin 90⁰+Cos 90⁰

Solution: As we know, Sin 90⁰=1

And Cos 90⁰=0

Therefore, Sin 90⁰+Cos 90⁰ = 1+0 = 1

Example: Find the value of Sin 270°+2Tan 45⁰

Solution: Sin 270°= -1

And Tan 45⁰=1

Therefore, Sin 270°+2Tan 45⁰ = -1+2*1 = -1+2 = 1

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