How do you convert $(12, .75)$ $(12,.75)$ to rectangular form?

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Answer 1 · 2018-07-19T12:29:36

Rectangular coordinates are $(8.18, 8.78)$ $color(cyan)((8.18, 8.78)$

$r = 12, θ = {0.75}^{c}$ $r = 12, theta = 0.75^c$

$x^{2} + y^{2} = r^{2}, \frac{x}{y} = tan θ$ $x^2 + y^2 = r^2, x/y = tan theta$

$x^{2} + y^{2} = 144$ $x^2 + y^2 = 144$

$\frac{x}{y} = tan (0.75) = 0.9316, x = 0.9316 y$ $x / y = tan (0.75) = 0.9316, x = 0.9316 y$

${(0.9316 y)}^{2} + y^{2} = 144$ $(0.9316y)^2 + y^2 = 144$

$0.8679 y^{2} + y^{2} = 144$ $0.8679y^2 + y^2 = 144$

$y^{2} = (\frac{144}{1.8679})$ $y^2 = (144 / 1.8679)$

$y \approx 8.78$ $y ~~ 8.78$

$x = 0.9316 \cdot 8.78 \approx 8.18$ $x = 0.9316 * 8.78 ~~ 8.18$

How do you convert (12,.75) (12,.75) (12,.75) to rectangular form?