I need to solve for theta when A/G=sin theta - Ucos theta?

Question

This is an equation for the acceleration of an object on an incline. The angle of the incline is theta, g is positive and is gravity, and u is the coefficient of friction. I know how to do this using a calculater by graphing but I don't want to. I want an EQUATION for theta, not a method to solve for it. Thanks for any help.

Answer 1

As 0 sqrt(1-sin^2 theta)
and calling sin theta =z
A/G-z= -Usqrt(1-z^2)
Squarin both sides you´ll get a 2nd degree equation in z which solved gives you sin theta and oso theta in the intervall 0-90 deg

Answer 2

remedy for cos(theta) cos(theta) = a million + sin(theta) replace interior the identity cos²(theta) + sin²(theta) = a million (a million + sin(theta))² + sin²(theta) = a million a million + 2sin(theta) + sin²(theta) + sin²(theta) = a million 2sin²(theta) + 2sin(theta) = 0 2sin(theta) (sin(theta) + a million) = 0 a product is 0 if are 0 its aspects sin(theta) = 0 sin(theta) + a million = 0 ? sin(theta) = - a million theta = 0, pi, (3/2) pi, 2pi