URGENT! Need help with some CAST and quadrant problems?

Question

Given sin x=root3 /2 for the acute angle x, determine the following trigonometric functions:

a. i. sin(2pi-x) ii. sin (pi+x) iii. sin (-x)

b. i. cos(pi-x) ii. cos (2pi+x) iii. cos(-x)

c. i. tan x ii. tan (pi-x) iii. tan (-x)

Answer 1

Find angle x= arcsin(√3 /2)= pi/3=60

Based on a 60-30- right triangle

With sides 1,√3, and 2 or 1/2,√3/2, and 1

a.i. sin(2pi-pi/3) = sin 5pi/3= -√3 /2

a.ii. sin (pi+pi/3) = sin 4pi/3 = -√3/2

a.iii sin (-pi/3) = -√3/2

b.i. cos(pi-pi/3)= -1/2

b.ii cos(2pi+pi/3) = 1/2

b.iii cos(-pi/3)= 1/2

c.i tan(pi/3) = √3

c.ii tan(pi-pi/3)= -√3

c.iii tan(-pi/3) = -√3