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# The spherical coordinates of (-3, 4, -12) are (rho, theta, phi). Find tan*theta + theta*phi.

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The spherical coordinates of (-3, 4, -12) are (rho, theta, phi). Find tan*theta + theta*phi.

I've already tried converting the cartesian coordinates provided into spherical coordinates:

I got rho = 13, theta = arccos(-12/13), and phi = arctan(-4/3)

I'm not sure how to add theta and phi together, I'm not sure if I converted them correctly at all.

Jun 16, 2020

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Yes, you have converted them correctly. But do you mean $$\tan\left(\theta + \varphi\right)$$ instead? Because you asked how to add theta and phi together.

Here is how you add theta and phi. You first convert the arccos in theta to arctan with trigonometry. Then you can use the formula $$\arctan A + \arctan B = \arctan \dfrac{A + B}{1 - AB}$$

Jun 17, 2020