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# 1298cosx=2770sinx+325.8

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1298cosx=2770sinx+325.8

Guest Oct 16, 2014

#2
+20025
+10

1298cosx=2770sinx+325.8

$$\begin{array}{rcl} 1298*cos(x) &=& 2770*sin(x)+325.8\\ \underbrace{1298}_{x_p}*\underbrace{cos(x)}_{n_x} -\underbrace{2770}_{y_p}*\underbrace{sin(x)}_{n_y} &=& \underbrace{325.8}_d \qquad \text{line: } \vec{p}*\vec{n}=d \quad \vec{p}=(x_p,y_p)=(1298,-2770) \\ \tan{(\alpha)} &=& \frac{y_p}{x_p} = -\frac{2770}{1298}\\\\ cos(x-\alpha) &=& \frac{d}{ \sqrt{x_p^2+y_p^2} } \\\\ sin(x-\alpha) &=& \frac{ \sqrt{x_p^2+y_p^2-d^2}}{\sqrt{x_p^2+y_p^2} }\\\\ tan(x-\alpha) &=& \pm \sqrt{\frac{ x_p^2+y_p^2 }{d^2} -1 )} \\\\ x_{1,2} -\alpha &=& tan^{-1} { \left( \pm \sqrt{\frac{ x_p^2+y_p^2 }{d^2} -1 \right) } }\\\\ x_{1,2} &=& \alpha + tan^{-1} { \left( \pm \sqrt{\frac{ x_p^2+y_p^2 }{d^2} -1 \right) } }\\\\ x_{1,2} &=& tan^{-1} { \left( \frac{y_p}{x_p} \right) } + tan^{-1} { \left( \pm \sqrt{\frac{ x_p^2+y_p^2 }{d^2} -1 \right) } }\\\\ x_{1,2} &=& tan^{-1} { \left( \frac{-2770}{1298} \right) } + tan^{-1} { \left( \pm \sqrt{\frac{ (1298)^2+(-2770)^2 }{(325.8)^2} -1 \right) } }\\\\ x_{1,2} &=& ( -64.8925847874\ensurement{^{\circ}} \pm n*\pi) +(\pm 83.8861674476\ensurement{^{\circ}} \pm n*\pi)\\\\ x_1 &=& -64.8925847874\ensurement{^{\circ}} + 83.8861674476\ensurement{^{\circ}} \pm n*2\pi\\\\ x_2 &=& -64.8925847874\ensurement{^{\circ}} - 83.8861674476\ensurement{^{\circ}} \pm n*2\pi\\\\ x_1 &=& 18.9935826602\ensurement{^{\circ}} \pm n*2\pi\\\\ x_2 &=& -148.778752235\ensurement{^{\circ}} \pm n*2\pi \end{array}$$

heureka  Oct 16, 2014
#1
+27056
+5

See if the following graph helps

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Alan  Oct 16, 2014
#2
+20025
+10

1298cosx=2770sinx+325.8

$$\begin{array}{rcl} 1298*cos(x) &=& 2770*sin(x)+325.8\\ \underbrace{1298}_{x_p}*\underbrace{cos(x)}_{n_x} -\underbrace{2770}_{y_p}*\underbrace{sin(x)}_{n_y} &=& \underbrace{325.8}_d \qquad \text{line: } \vec{p}*\vec{n}=d \quad \vec{p}=(x_p,y_p)=(1298,-2770) \\ \tan{(\alpha)} &=& \frac{y_p}{x_p} = -\frac{2770}{1298}\\\\ cos(x-\alpha) &=& \frac{d}{ \sqrt{x_p^2+y_p^2} } \\\\ sin(x-\alpha) &=& \frac{ \sqrt{x_p^2+y_p^2-d^2}}{\sqrt{x_p^2+y_p^2} }\\\\ tan(x-\alpha) &=& \pm \sqrt{\frac{ x_p^2+y_p^2 }{d^2} -1 )} \\\\ x_{1,2} -\alpha &=& tan^{-1} { \left( \pm \sqrt{\frac{ x_p^2+y_p^2 }{d^2} -1 \right) } }\\\\ x_{1,2} &=& \alpha + tan^{-1} { \left( \pm \sqrt{\frac{ x_p^2+y_p^2 }{d^2} -1 \right) } }\\\\ x_{1,2} &=& tan^{-1} { \left( \frac{y_p}{x_p} \right) } + tan^{-1} { \left( \pm \sqrt{\frac{ x_p^2+y_p^2 }{d^2} -1 \right) } }\\\\ x_{1,2} &=& tan^{-1} { \left( \frac{-2770}{1298} \right) } + tan^{-1} { \left( \pm \sqrt{\frac{ (1298)^2+(-2770)^2 }{(325.8)^2} -1 \right) } }\\\\ x_{1,2} &=& ( -64.8925847874\ensurement{^{\circ}} \pm n*\pi) +(\pm 83.8861674476\ensurement{^{\circ}} \pm n*\pi)\\\\ x_1 &=& -64.8925847874\ensurement{^{\circ}} + 83.8861674476\ensurement{^{\circ}} \pm n*2\pi\\\\ x_2 &=& -64.8925847874\ensurement{^{\circ}} - 83.8861674476\ensurement{^{\circ}} \pm n*2\pi\\\\ x_1 &=& 18.9935826602\ensurement{^{\circ}} \pm n*2\pi\\\\ x_2 &=& -148.778752235\ensurement{^{\circ}} \pm n*2\pi \end{array}$$

heureka  Oct 16, 2014
#3
+93683
0

Very impressive Heureka :)

Melody  Oct 16, 2014