Stitz-Zeager_College_Algebra_e-book

However 0 0 could be 0 or it could be neither of which

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Unformatted text preview: (θ) = ± sin(α) = ± 13 . Since the terminal side of θ falls in Quadrant III, both cos(θ) and sin(θ) are negative, 5 12 hence, cos(θ) = − 13 and sin(θ) = − 13 . 7 Since π + α = α + π , θ may be plotted by reversing the order of rotations given here. You should do this. 10.2 The Unit Circle: Cosine and Sine 621 y y 1 1 θ θ π 1 α x 1 α Visualizing θ = π + α x θ has reference angle α (b) Rewriting θ = 2π − α as θ = 2π + (−α), we can plot θ by visualizing one complete revolution counter-clockwise followed by a clockwise revolution, or ‘backing up,’ of α radians. We see that α is θ’s reference angle, and since θ is a Quadrant IV angle, the 5 Reference Angle Theorem gives: cos(θ) = 13 and sin(θ) = − 12 . 13 y y 1 1 θ θ 2π 1 −α Visualizing θ = 2π − α x 1 x α θ has reference angle α (c) Taking a cue from the previous problem, we rewrite θ = 3π − α as θ = 3π + (−α). The angle 3π represents one and a half revolutions counter-clockwise, so that when we ‘back up’ α radians, we end up in Q...
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