Solveeit Logo
Login

Question

Question: Find the values of \(\sin \dfrac{5\pi }{3}\)...

Find the values of sin⁡5π3\sin \dfrac{5\pi }{3}

Explanation

Solution

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⁡5π3\sin \dfrac{5\pi }{3}
Multiply by 180π\dfrac{180}{\pi } to find the degrees of angle, we get:
=sin⁡5π3×180π=\sin \dfrac{5\pi }{3}\times \dfrac{180}{\pi }
By simplifying the expression above, we convert it into:
=sin⁡300=\sin 300
To make it into range of 0 to 90, we can write it as:
=sin⁡(360−60)=\sin \left( 360-60 \right)
By basic knowledge of trigonometry, =sin⁡(360−x)=−sin⁡x=\sin \left( 360-x \right)=-\sin x
By applying this to our expression, we get it as:
=−sin⁡60∘=-\sin 60{}^\circ
By substituting the known value, we get it as:
=−32=−0.8660254=-\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 180π{\dfrac{180}{\pi}} radians.Similarly To convert from degrees to radians, multiply the degrees by π180{\dfrac{\pi}{180}} radians.Students should remember trigonometric ratios,formulas and standard angles to solve these types of questions.