Link to home
Start Free TrialLog in
Avatar of phoffric
phoffric

asked on

How to solve a trigonometry equation

In another question, I had solved a problem of 4 equations in 4 unknowns numerically by using plot utilities. (Another expert used Excel Solver to solve the equations.)
https://www.experts-exchange.com/questions/28929349/Solve-the-following-simultaneous-equations.html?anchorAnswerId=41483976#a41483976

Getting the answer for alpha is not the question as we already know the value. This question is asking for the algebraic and/or trigonometric steps in getting the answer that WolframAlpha shows below for the following equation:
cos ( 85 * pi/180 - alpha)/ cos ( alpha ) = 2

Open in new window


Can someone show the steps as to how Wolfram got their solution?
http://www.wolframalpha.com/input/?i=cos+(+85+*+pi%2F180+-+alpha)%2F+cos+(+alpha+)+%3D+2

Here is the Wolfram answer (but no steps shown):
User generated imageIf someone has WolframAlpha Pro, then possibly their Step-By-Step solution will be good.
SOLUTION
Avatar of Kyle Hamilton
Kyle Hamilton
Flag of United States of America image

Link to home
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
Start Free Trial
SOLUTION
Avatar of crystal (strive4peace) - Microsoft MVP, Access
crystal (strive4peace) - Microsoft MVP, Access

Link to home
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
Start Free Trial
Do you really need a symbolic solution or float64 is enough?
Can you draw both triangles? Then solution is obvious.
Avatar of phoffric
phoffric

ASKER

Thanks, Kyle Hamilton, for posting the WA solution. I would have accepted it immediately but for one missing step. WA didn't show the steps transforming the equation
cos ( 85 * pi/180 - alpha)/ cos ( alpha ) = 2

Open in new window

to
sec(alpha) sin(pi/36 + alpha) = 2

Open in new window

I scratched out something quickly, but was off by a minus sign, so for completeness it would be useful to get the missing steps. (If no detailed response, I'll work out my mistake as soon as I have some time.)
ASKER CERTIFIED SOLUTION
Link to home
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
Start Free Trial
Thanks, Kyle Hamilton, for taking the time to find the WA solution.
Solutions always look easy after you get the hint.