Question

Find the values of $\sin \dfrac{5\pi }{3}$

Answer 1

Hint:Convert the radians into degrees. Then, as we only have the values of angle in the range 0 to 90. Convert the sine into that range. Now use the value of sine as you know to find the answer.

Complete step-by-step answer:
 Given expression in the question for which we need to value:
$\sin \dfrac{5\pi }{3}$
Multiply by $\dfrac{180}{\pi }$ to find the degrees of angle, we get:
$=\sin \dfrac{5\pi }{3}\times \dfrac{180}{\pi }$
By simplifying the expression above, we convert it into:
$=\sin 300$
To make it into range of 0 to 90, we can write it as:
$=\sin \left( 360-60 \right)$
By basic knowledge of trigonometry, $=\sin \left( 360-x \right)=-\sin x$
By applying this to our expression, we get it as:
$=-\sin 60{}^\circ $
By substituting the known value, we get it as:
$=-\dfrac{\sqrt{3}}{2}=-0.8660254$
The above value is the exact value of the given expression.

Note: Whenever you see a value of angle greater than 90, try to bring it into range you know to substitute the values.To convert from radians to degrees, multiply the radians by ${\dfrac{180}{\pi}}$ radians.Similarly To convert from degrees to radians, multiply the degrees by ${\dfrac{\pi}{180}}$ radians.Students should remember trigonometric ratios,formulas and standard angles to solve these types of questions.