Unit 3 Assessment.docx - TVO ILC MHF4U Unit 3 Assessment...

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Unit 3 Assessment 1. Determine the following: [K4] a. Given a sector with an arc length of 4.5 cm and a radius of 3 cm, find the angle subtended by the arc. a = 4.5 cm r = 3 cm θ = a r θ = 4.5 3 1.5 radians b. Given a sector with an angle of 13 radians and a radius of 7 m, find the arc length. θ = 13 radians r = 7 m a = θ∙r a = 13 7 a = 91 cm 2. Fill in the table. Show your work and keep answers exact. [K4] Degrees Radians 23 π 18 180 ° = 8 ° _ 2 π 45 230 0 230 °∙ π 180 = 23 π 180 TVO ILC MHF4U Unit 3 Assessment Copyright © 2019 The Ontario Educational Communications Authority. All rights reserved. 1
3. Determine the values of θ if 0 ≤ θ ≤ 2 π given that cosx = − 0.3178 . Explain your process. [K4], [C2] co s 1 ( 0.3178 ) = x 1.89420 = x Cosine is negative on quadrants 2 and 3 Quadrant 2: Quadrant 3: θ 1 = π x θ 2 = π + x ¿ π 1.89420 ¿ π + 1.89420 ¿ 1.24739 ¿ 5.03579 4. Determine exact values of θ if 0 ≤ θ ≤ 2 π given that tanθ = − 3 . Explain your process. [K4], [C2] 3 ( ¿ )= x tan 1 ¿ π 3 = x Tangent is negative on quadrants 2 and 4 Quadrant 2: Quadrant 4: θ 1 = π x θ 2 = 2 π x ¿ π π 3 ¿ 2 π π 3 ¿ 2 π 3 ¿ 5 π 3 5. Describe the transformations on the given cosine function.

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