Stitz-Zeager_College_Algebra_e-book

Applying the even identity of cosine we get cos0 0

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Unformatted text preview: uadrant II. Using the Reference Angle Theorem, we get 5 cos(α) = − 13 and sin(α) = 12 . 13 622 Foundations of Trigonometry y y 1 1 θ −α α 3π x 1 Visualizing 3π − α 1 x θ has reference angle α π 2 π 2 (d) To plot θ = + α, we first rotate radians and follow up with α radians. The reference angle here is not α, so The Reference Angle Theorem is not immediately applicable. (It’s important that you see why this is the case. Take a moment to think about this before reading on.) Let Q(x, y ) be the point on the terminal side of θ which lies on the Unit Circle so that x = cos(θ) and y = sin(θ). Once we graph α in standard position, we use the fact that equal angles subtend equal chords to show that the dotted lines in 12 5 the figure below are equal. Hence, x = cos(θ) = − 13 . Similarly, we find y = sin(θ) = 13 . y y 1 1 θ α π 2 π 2 5 12 13 , 13 α Q (x, y ) 1 Visualizing θ = P +α x α 1 x Using symmetry to determine Q(x, y ) Our next example asks us to solve some very basic trigonometric equations.8 8 We will mo...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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