Question

Evaluate each expression.

Answer 1

Evaluate each expression.
\[Sin\frac{5\pi}{3}\]

Answer 2

sin((`)/(3))

Take the sine of (`)/(3) to get (~(3))/(2).
(~(3))/(2)
~ means square root
' means pi

Answer 3

and similarly

Answer 4

sin((5`)/(3))

Take the sine of (5`)/(3) to get -(~(3))/(2).
-(~(3))/(2)

Answer 5

sin((5`)/(3))

To find whether the value of sin((5`)/(3)) is negative or positive, setup a triangle that represents the unit circle based on the definition of sin.
T[,90,(5`)/(3),-(~(3))/(2),(1)/(2),1,,,]

Find the value using the definition sin((5`)/(3))=(opp)/(hyp).
sin((5`)/(3))=(opp)/(hyp)=(-(~(3))/(2))/((1)/(2))

To divide by (1)/(2), multiply by the reciprocal of the fraction.
sin((5`)/(3))=(opp)/(hyp)=2*-(~(3))/(2)

Remove the common factor of 2 from the numerator of the first expression and denominator of the second expression.
sin((5`)/(3))=(opp)/(hyp)=-~(3)