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Stitz-Zeager_College_Algebra_e-book

# The amplitude of the sinusoid is a measure of how

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Unformatted text preview: . The latter form 3 of the solution is best understood looking at the geometry of the situation in the diagram below.3 3 See Example 10.2.5 number 3 in Section 10.2 for another example of this kind of simpliﬁcation of the solution. 10.3 The Six Circular Functions and Fundamental Identities y 1 639 y 1 π 3 x 1 x 1 π 3 3. From the table of common values, we see that π has a cotangent of 1, which means the 4 solutions to cot(θ) = −1 have a reference angle of π . To ﬁnd the quadrants in which our 4 solutions lie, we note that cot(θ) = x , for a point (x, y ), y = 0, on the Unit Circle. If cot(θ) is y negative, then x and y must have diﬀerent signs (i.e., one positive and one negative.) Hence, π our solutions lie in Quadrants II and IV. Our Quadrant II solution is θ = 34 + 2πk , and for π Quadrant IV, we get θ = 74 + 2πk for integers k . Can these lists be combined? We see that, π in fact, they can. One way to capture all the solutions is: θ = 34 + πk for integers k . y 1 y 1 π 4 x 1 π 4 x 1 We have already seen the importan...
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