Stitz-Zeager_College_Algebra_e-book

# Suppose k and j are whole numbers between 0 and n 1

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Unformatted text preview: cos(2θ) ranges from 0 to 1 as well.7 From this, we know r = ±4 cos(2θ) ranges continuously from 0 to ±4, respectively. Below we graph both r = 4 cos(2θ) and r = −4 cos(2θ) on the θr plane and use them to sketch the corresponding pieces of the curve r2 = 16 cos(2θ) in the xy -plane. As we have seen in earlier 7 Owing to the relationship between y = x and y = former is deﬁned. √ x over [0, 1], we also know cos(2θ) ≥ cos(2θ) wherever the 808 Applications of Trigonometry π examples, the lines θ = π and θ = 34 , which are the zeros of the functions r = ±4 4 serve as guides for us to draw the curve as is passes through the origin. cos(2θ), y r θ= 4 1 π 2 π 3π 4 2 θ= 3 4 π 4 3π 4 π 4 1 x θ 2 3 4 −4 r = 4 cos(2θ) and r = −4 cos(2θ ) As we plot points corresponding to values of θ outside of the interval [0, π ], we ﬁnd ourselves retracing parts of the curve,8 so our ﬁnal answer is below. y r θ= 4 π 4 π 2 3π 4 −4 π θ 3π 4 4 −4 θ= 4 π 4 x −4 r = ±4 cos(2θ) in the θr-plane r2 = 16 cos(2θ) in the xy...
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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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