Questions on Unit Circles in Trigonometry

Multiple choice questions on unit circle in trigonometry with answers at the bottom of the page.

Question 1

Which of the following points is in the unit circle?
a) (-√2 / 2 , -√2 / 2)
b) (√2 / 3 , -√2 / 3)
c) (1 / 2 , 1 / 2)
d) (3 / 2 , 2 / 3)

Question 2

A point is in Quadrant-III and on the Unit Circle. If its x-coordinate is -4 / 5, what is the y-coordinate of the point?
a) 3 / 5
b) -3 / 5
c) -2 / 5
d) 5 / 3

Question 3

Find the point on the Unit Circle associated with the rotation -9π/2
a) (0 , -1)
b) (0 , 1)
c) (1 , 0)
d) (-1 , 0)

Question 4

Find the point on the Unit Circle associated with the angle 5π/3
a) (1 / 2 , 1 / 2)
b) (-√3 / 2 , 1/2)
c) (1 / 2 , -√3 / 2)
d) (-√3 / 2 , -1/2)

Question 5

If point (a , b) is on the Unit Circle associated with the rotation t, which of the following is not correct?
a) sin(t) = b
b) cos(t) = a
c) sin(-t) = - a
d) cos(-t) = - a

Question 6

If point (a , b) is on the Unit Circle associated with the rotation t and point (c , d) is also on the Unit circle associated with rotation t + π, then which of the following is correct?
a) c = - a and d = - b
b) c = - a and d = b
c) c = a and d = b
d) c = a and d = - b

Question 7

If point (a , b) is on the Unit Circle associated with the rotation t, then the point on the Unit circle associated with rotation t + π / 2, has the following coordinates
a) (b , a)
b) (-b , a)
c) (-b , -a)
d) (-a , b)

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