Question

How do you evaluate $\sin \left( 0 \right)$ ?

Answer 1

Hint: Here for evaluating the value of $\sin \left( 0 \right)$ , we need to know the ratio by which it is divided. As we know sine is equal to the perpendicular side upon the hypotenuses. So by using this statement we will evaluate the value of $\sin \left( 0 \right)$ .

Complete step-by-step answer:
So we have to evaluate the value for $\sin \left( 0 \right)$ , first of all, we need to check the coordinate points which will be on the $x$ and $y$ plane. Here, the $\sin \left( 0 \right)$ will denote that the value for the $x$ coordinate will be equal to $1$ and the value for the $y$ coordinate will be equal to $0$ .
Hence, the coordinates can be written as $\left( {1,0} \right)$ . So from this, as we know sine is equal to the perpendicular side upon the hypotenuses. So on substituting the values, we will get the equation as
\[ \Rightarrow \sin {0^ \circ } = \dfrac{0}{1}\]
And as we know that, when zero is divided from any number it gives back zero only. Hence on solving the above line, we will get
\[ \Rightarrow \sin {0^ \circ } = 0\]
Hence, the value of $\sin \left( 0 \right)$ has been evaluated and it will be, \[\sin {0^ \circ } = 0\] .

Additional information:
In a right-angled triangle, the side which is opposite to the longest side of the triangle will be termed as the hypotenuse and the side which will be opposite of the angle theta then it will be termed as the opposite. And similarly, the near side which will lie just after an angle will be termed as Adjacent.

Note: From the ratio of sine, if we reverse the values or we can if we take the opposite of it then we will get the value for the cos. And similarly, if we want to write the value for tangent then we can get the value of sine and cos from there.