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Stitz-Zeager_College_Algebra_e-book

# Example 11101 sketch the curve described by x t2 3 y

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Unformatted text preview: 3 2 sin(θ) is an ellipse directrix y = 3 , vertices (0, 1), (0, −3) center (0, −2) , foci√ , 0), (0, −2) (0 minor axis length 2 3 y y 4 4 3 3 2 2 1 1 −4 −3 −2 −1 1 2 3 4 x −1 −4 −3 −2 −1 1 2 3 4 x −1 −2 −2 −3 −4 −4 6 is the ellipse 3−cos(θ+ π ) 4 6 r = 3−cos(θ) = 1− 1 2 θ) cos( 3 rotated through φ = − π 4 4 (c) r = 1+3 cos(θ) is a hyperbola 4 directrix x = 3 , vertices (1, 0), (2, 0) 3 center 2 , 0 , foci (0, 0), (3, 0) √ conjugate axis length 2 2 (d) r = y y 4 4 3 3 2 2 1 1 −4 −3 −2 −1 1 2 3 4 x −4 −3 −2 −1 y 1 −1 −2 −2 −3 −4 3 4 −3 −4 2 x −1 φ = −π 4 x 842 Applications of Trigonometry 11.7 Polar Form of Complex Numbers In this section, we return to our study of complex numbers which were ﬁrst introduced in Section 3.4. Recall that a complex number is a number √ the form z = a + bi where a and b are real of numbers and i is the imaginary unit deﬁned by i = −1. The number a is called the real part o...
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