Question

How do you find the value of \[\sin 60\] ?

Answer 1

Hint: In this question, the value of \[\sin 60\] is obtained by considering this as the triangle that has the respective angle and then finds the value of the corresponding sine angle. The last step is to rationalize the fraction obtained.

Complete Step by Step solution:
As we know that the trigonometry is the part of calculus and the basic ratio of trigonometric are sine and cosine which have their application in sound and light wave theories. The trigonometric have vast applications in naval engineering such as to determine the height of the wave and the tide in the ocean. Three important functions of trigonometry are sin, cosine and tangent.

In this question, we have given a trigonometric ratio as \[\sin 60\] and we need to calculate its value.
The sine angle in a right-angle triangle is the ratio perpendicular to the hypotenuse of the triangle.
\[ \Rightarrow \sin \theta = \dfrac{{perpendicular}}{{hypotenuse}}\]
Let us consider the sine values for the different angle as given below,
\[
  \sin 0^\circ = 0 \\
  \sin 30^\circ = \dfrac{1}{2} \\
  \sin 45^\circ = \dfrac{1}{2} \\
  \sin 60^\circ = \dfrac{{\sqrt 3 }}{2} \\
  \sin 90^\circ = 1 \\
 \]
As we can see from the above values, the value of $\sin 60^\circ $ is \[\sin 60^\circ = \dfrac{{\sqrt 3 }}{2}\].

Thus, the value of \[\sin 60^\circ = \dfrac{{\sqrt 3 }}{2}\].

Note:
As we know that the radian measure is defined as the ratio of the length of the circular arc to the radius of the arc, the measure of the angle is determined by the rotation from the initial side to the final side, and the angle is measured in degrees and in trigonometry the degree measure is \[\dfrac{1}{{{{360}^{{\text{th}}}}}}\] of the complete rotation.