Unformatted text preview: uadrant II. Using the Reference Angle Theorem, we get
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 (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
the ﬁgure below are equal. Hence, x = cos(θ) = − 13 . Similarly, we ﬁnd y = sin(θ) = 13 .
y y 1 1 θ
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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