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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