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 \[\dfrac{\sqrt{3}}{2}\] .
Hence we get the value of \[\sin 120\] is \[\dfrac{\sqrt{3}}{2}\].
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 \[\dfrac{\sqrt{3}}{2}\] .

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 \[\sin (90^{o} + x)\ = cos\ x\]
Therefore we get,
\[\sin 120^{o}= \cos 30^{o}\]
We know that the value of \[cos 30^{o}\] is \[\dfrac{\sqrt{3}}{2}\] .
Thus we get, the value of \[\sin 120^{o} = \dfrac{\sqrt{3}}{2}\ \]