Use the fact that the trigonometric functions are periodic t

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. sin 17 pi/3 - squareroot 3/2 squareroot 3/2 -1 -1/2

Solution

sin 17pi/3

period of a sine function is 2pi

so we can write

17pi/3 = 4pi + 5pi/3

sin 5pi/3 = -sin (pi/3) ( reference angle )

sin pi/3 = sqrt 3/2

sin (5pi/3) = - sqrt 3/2

therefore,

sin 17pi/3 = - sqrt 3/2

option 1