# Trig Equation

The last step in a problem of mine is to find all solutions between 0 and pi/2 of the following equation:
R(tanx + 1/cosx + x - 1) = 1/2R2(tanx - x)

By simple inspection and with the aid of a graphing calculator, its obvious that the only solution is x=0, regardless of the value of R. This is enough for the assignment, but Im wondering if theres a way to mathematically isolate x and prove that 0 is the only solution

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HallsofIvy
Homework Helper
With t both inside and outside the trig functions (and do you really mean to have t on one side and x on the other?), there is no "algebraic" method of solving this equation.

Thanks, I thought there might have been a useful identity, but it looks like the graphing calculator will do.

AlephZero
Homework Helper
The last step in a problem of mine is to find all solutions between 0 and pi/2 of the following equation:
R(tanx + 1/cosx + x - 1) = 1/2R2(tanx - x)

By simple inspection and with the aid of a graphing calculator, its obvious that the only solution is x=0, regardless of the value of R.
Not true. For example when R = 0.3 there's a root close to x = 0.6

If you rearrange it as (tan x - x ) / (tan x + 1/cos x + x - 1) = 2R^3, then it's obvious that for any value of x=X between 0 and pi/2 there is some value of R that makes X a solution of the equation.

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Ive got another question, so Ill put it in here. As we know, the wrapping function takes a point (1,a) on a number line and wraps it about a unit circle until it gets to the point (cosa, sina).

Today on a test, we were asked to find the parametric form of the path of the point from t=0 to t=a. No one got it and well go over it next week, but Im anxious to know how to solve something like this. Ive only dealt with parametric lines and the path is obviously not a line. I started to mess around with polar graphs in my calculator, but nothing comes close. Is it a logarithmic spiral?

Ive got another question, so Ill put it in here. As we know, the wrapping function takes a point (1,a) on a number line and wraps it about a unit circle until it gets to the point (cosa, sina).

Today on a test, we were asked to find the parametric form of the path of the point from t=0 to t=a. No one got it and well go over it next week, but Im anxious to know how to solve something like this. Ive only dealt with parametric lines and the path is obviously not a line. I started to mess around with polar graphs in my calculator, but nothing comes close. Is it a logarithmic spiral?