6.1. Angles of Rotation (Coterminal Angle, RAA).notebook May 28, 2014 Unit 6 Trigonometry II Lesson 1: Angles of Rotation Grade 10: Solve sinθ = 0.866 Looking at the sine function, where θ is the angle and y is the trig ratio, we see that there are more possible answers since y = sinθ is periodic. ∴ θ = are all solutions to the trig equation sinθ = 0.866 because we o must take into account all angles < 0 and > 90.o 6.1. Angles of Rotation (Coterminal Angle, RAA).notebook May 28, 2014 Angles of Rotation We use the cartesian plane to account for angles greater than o 90 . Counter clockwise rotation shows a positive angle. Clockwise rotation shows a negative angle. The rotation is indicated by a directed arrow starting at the positive xaxis (θ is in standard position). Ex.1. State the angle of rotation. (b) a) 60 o 60 (c) o o 45 Two angles in standard position are coterminal if they have the same terminal arm. Coterminal angles differ by a multiple o of 360. ∴ Examples a & b above are coterminal. 6.1. Angles of Rotation (Coterminal Angle, RAA).notebook May 28, 2014 o Ex.2. Find three angles coterminal with 80 . Ex.3. For angles α and θ, determine if they are coterminal o o a) α = 57 θ = 1137 o (b) α = 340 θ = 400 o 6.1. Angles of Rotation (Coterminal Angle, RAA).notebook May 28, 2014 Angles of any measure have a Related Acute Angle (β) associated with them. The RAA (β) is the acute (less than 90 ) angle (can be shown in a ) that is formed between the terminal arm and the xaxis. We always draw a line up/down to the xaxis. This drawn is very useful in trigonometry Ex.4. Find the RAA, β, for each angle θ. Draw the line with the xaxis. Quadrant I Quadrant II β β Quadrant III β β Quadrant IV 6.1. Angles of Rotation (Coterminal Angle, RAA).notebook May 28, 2014 Homework: 1. Handout: Angles of Rotation 2. Handout: Exercise 7.2. # 1ad, 2abe, 3, 4acg 3. Calculate all ratios of Handout "Cast Rule to solve simple trig equations"

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