Stitz-Zeager_College_Algebra_e-book

# 1 this gives sint 4x2 1 so that cost cott sint

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Unformatted text preview: 3θ) as a polynomial in terms of cos(θ). Solution. 1. Using Theorem 10.3 from Section 10.2 with x = −3 and y = 4, we ﬁnd r = x2 + y 2 = 5. 3 Hence, cos(θ) = − 5 and sin(θ) = 4 . Applying Theorem 10.17, we get cos(2θ) = cos2 (θ) − 5 2 2 7 4 3 sin2 (θ) = − 3 − 4 = − 25 , and sin(2θ) = 2 sin(θ) cos(θ) = 2 5 − 5 = − 24 . Since both 5 5 25 cosine and sine of 2θ are negative, the terminal side of 2θ, when plotted in standard position, lies in Quadrant III. 662 Foundations of Trigonometry 2. If your ﬁrst reaction to ‘sin(θ) = x’ is ‘No it’s not, cos(θ) = x!’ then you have indeed learned something, and we take comfort in that. However, context is everything. Here, ‘x’ is just a variable - it does not necessarily represent the x-coordinate of the point on The Unit Circle which lies on the terminal side of θ, assuming θ is drawn in standard position. Here, x represents the quantity sin(θ), and what we wish to know is how to express sin(2θ) in terms of x. We will see more of this kind of thing in Section 10.6, and,...
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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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