Question

What is $$\sin 120$$ degrees ?

Answer 1

Hint: In this question, we need to find the value of $$\sin {120}^o$$ . We can find the value of $$sin{120}^o$$ by using trigonometric identities and values. Sine is nothing but a ratio of the opposite side of a right angle to the hypotenuse of the right angle. The basic trigonometric functions are sine , cosine and tangent. The value of $$sin{60}^o$$ is used to find the value. With the help of the Trigonometric functions , we can find the value of $$\sin {120}^o$$ .

Complete step-by-step solution:
Here need to find the value of $$\sin {120}^o$$,
We can find the value of $$\sin {120}^o$$ by using other angles of sine functions.
We can rewrite $${120}^o$$ as $${180}^o–{60}^o$$
Thus we get,
$$\sin {120}^o=\sin ({180}^o–{60}^o)$$
We know that $$\sin ({180}^o–x)=\sin x$$ ,
Therefore we get,
$$\sin {120}^o=\sin {60}^o$$
We know that the value of $$\sin {60}^o$$ is equal to $${\displaystyle \frac{\sqrt{3}}{2}}$$ .
Hence we get the value of $$\sin 120$$ is $${\displaystyle \frac{\sqrt{3}}{2}}$$.
Thus we can say that the value of $$\sin {60}^o$$ is equal to the value of $$\sin {120}^o$$
Final answer :
The value of $$\sin {120}^o$$ is $${\displaystyle \frac{\sqrt{3}}{2}}$$ .

Note: The concept used in this problem is trigonometric identities and ratios. Trigonometric identities are nothing but they involve trigonometric functions including variables and constants. The common technique used in this problem is the use of trigonometric functions. Geometrically, $$\sin {120}^o$$ lies in the second quadrant. Hence the value of $$\sin {120}^o$$ is non-negative.
Alternative solution :
We can find the value of $$\sin {120}^o$$ by using the values of cosine functions .
We can also rewrite $${120}^o$$ as $$({90}^o+{30}^o)$$
Thus we get,
$$\sin {120}^o=\sin ({90}^o+{30}^o)$$
We know that $$\sin ({90}^o+x)=cosx$$
Therefore we get,
$$\sin {120}^o=\cos {30}^o$$
We know that the value of $$cos{30}^o$$ is $${\displaystyle \frac{\sqrt{3}}{2}}$$ .
Thus we get, the value of $$\sin {120}^o={\displaystyle \frac{\sqrt{3}}{2}}$$