Determine the exact value for the following trigonometric ratios.

Question

At the beginning of the lesson, the idea of a bicycle tire with a radius of 1 unit being used to determine the height of the marker after a rotation of a specific angle was presented. Determine the exact value for the following trigonometric ratios. Justify your answer for question 4c.

a. sin 5π/3

b. cos 5π/3

c. tan 5π/3

d. The marker on the bicycle tire is a point on the unit circle. Determine the coordinates of the marker if the angle of rotation is 5π/3.

Answer 1

sin5pi/3 = sin300= -sin60= -sqr3/2

cos5pi/3 = cos300 = 1/2

tan5pi/3 = tan300 = sin300/cos300 = -sqr3

in polar coordinates, that's (1, 5pi/3)

convert to rectangular coordinates

(1/2, -sqr3/2)= (cos(5pi/3), sin(5pi/3))