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Pre-Calc Homework Solutions 20

Pre-Calc Homework Solutions 20 - 20 Section 1.4 10(a 6(a 6...

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6. (a) [ 2 6, 6] by [ 2 4, 4] The graph is a circle of radius 2 centered at ( h , 0). As h changes, the graph shifts horizontally. (b) [ 2 6, 6] by [ 2 4, 4] The graph is a circle of radius 2 centered at (0, k ). At k changes, the graph shifts vertically. (c) Since the circle is to be centered at (2, 2 3), we use h 5 2 and k 5 2 3. Since a radius of 5 is desired, we need to change the coefficients of cos t and sin t to 5. x 5 5 cos t 1 2, y 5 5 sin t 2 3, 0 # t # 2 p (d) x 5 5 cos t 2 3, y 5 2 sin t 1 4, 0 # t # 2 p 7. (a) [ 2 3, 3] by [ 2 2, 2] Initial point: (1, 0) Terminal point: ( 2 1, 0) (b) x 2 1 y 2 5 cos 2 t 1 sin 2 t 5 1 The parametrized curve traces the upper half of the circle defined by x 2 1 y 2 5 1 (or all of the semicircle defined by y 5 ˇ 1 w 2 w x w 2 w ). 8. (a) [ 2 3, 3] by [ 2 2, 2] Initial and terminal point: (0, 1) (b) x 2 1 y 2 5 sin 2 (2 p t ) 1 cos 2 (2 p t ) 5 1 The parametrized curve traces all of the circle defined by x 2 1 y 2 5 1. 9. (a) [ 2 3, 3] by [ 2 2, 2] Initial point: ( 2 1, 0) Terminal point: (0, 1) (b) x 2 1 y 2 5 cos 2 ( p 2 t ) 1 sin 2 ( p 2 t ) 5 1 The parametrized curve traces the upper half of the circle defined by x 2 1 y 2 5 1 (or all of the semicircle defined by y 5 ˇ 1 w 2 w x w 2 w ). 10. (a) [ 2 4.7, 4.7] by [ 2 3.1, 3.1] Initial and terminal point: (4, 0)
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