Pre – Calculus Math 12
Worksheet (The Unit Circle)
YOU MUST SHOW YOUR WORK WHENEVER POSSIBLE!
1. Determine the equation of a circle with centre at the origin and given radius.
a) 12 units
b) 2.6 units
2. Is each point on the unit circle? How do you know?
 3 1
a)   , 
 4 4
 5 7
, 
b) 
 8 8
 5 12 
c)   , 
 13 13 
 4 3
d)  , 
 5 5
3. Determine the missing coordinate(s) for all points on the unit circle satisfying the given conditions. Draw a
diagram to support your answer.
 7 
a)   , y  in quadrant III
 8 
5

b)  x,   in quadrant IV
7

4. If P  is the point at the intersection of the terminal arm of angle θ and the unit circle, determine the exact
coordinates of each of the following. HINT: Draw a sketch.
a) P 
 
b) P 
3
 
c) P  
 6
 3 
d) P  
 4 
5. Identify a measure for the central angle θ in the interval 0 ≤ θ < 2π such that P  is the given point.
0,  1
1
3

b)  , 
2 
2

3 1
, 
c)  
2
2

 2
2

,
d) 

2
2


a)

3 1
,  .
6. Determine the smallest positive and negative measure for θ if P    
 2 2
 1 2 2
 , determine the following.
7. If P     , 
3 
 3
a) What does P(θ) represent? Explain using a
diagram.
b) In which quadrant does θ terminate?


c) Determine the coordinates of P   .
2



d) Determine the coordinates of P   .
2
