Find an equation in rectangular coordinates for the equation given in spherical coordinates. Express the coefficients to two decimal places. $$\theta = \frac { \pi } { 16 }$$
A) $y = 0.20 x$
B) $x = 0.20 y$
C) $y = 5.03 x$
D) $z = 0.20 x$
E) $\gamma = 0.20 z$

Question

Quizplus · Accepted Answer

In spherical coordinates, the angle $\theta$ is measured in the xy-plane from the positive x-axis toward the positive y-axis. The equation $\theta = \frac{\pi}{16}$ in rectangular coordinates (x, y, z) translates to a relationship between x and y, since $\theta$ involves these two axes. The relationship is given by $\tan(\theta) = \frac{y}{x}$, which simplifies to $y = x \tan(\theta)$. Substituting $\theta = \frac{\pi}{16}$, we get $y = x \tan\left(\frac{\pi}{16}\right)$. The value of $\tan\left(\frac{\pi}{16}\right)$ is approximately 0.20, leading to the equation $y = 0.20x$.

Find an Equation in Rectangular Coordinates for the Equation Given θ=π16\theta = \frac { \pi } { 16 }θ=16π​

Find an Equation in Rectangular Coordinates for the Equation Given $\theta = \frac { \pi } { 16 }$