# How to get θ sin and cos are together in 1 equation

b2cos2θ+2cosθ(-mb+bc2-bz-bcsinθ)+2sinθ(cm-cz)-c2sin2θ=p

How to get θ in terms of b,c,m,z,p
The equation i formed to calculate the dynamic
PLs, anyone can help to solve this, i would much appreciate! im doing my FYP!

## Answers and Replies

HallsofIvy
Science Advisor
Homework Helper
Replace $sin^2(\theta)$ with $1- cos^2(\theta)$ and $sin(\theta)$ with $\sqrt{1- cos^2(\theta)}$. That will give you an equation in $cos(\theta)$ only. However it will involve a square root so isolate that on one side of the equation and square both sides to get a fourth degree equation in $cos(\theta)$. That is not going to give a simple answer!

Thanks for ur precious reply! Somehow i still have to go through this question.. does it has any alternative method?

phyzguy
Science Advisor
HallsofIvy's approach is the right one. Do you know the values of b,c,m,z,p (or ranges)? The equation will be easily solved numerically if you do.

b,c,m,z,p are the fixed constant, they will be known later. Somehow i cant get θ if i use HallsofIvy's approach because the existence of fourth, third, second, first degree of cos θ

and also how if i want to use numerical method? how to use it ? Matlab?

phyzguy
Science Advisor
Personally, I use Mathematica, but Matlab will work. A simple Newton's method solver will find the root quickly once the coefficients are known.

may i know how do i use numerical method to solve this trigo+algebraic equation? i need to equate the equation θ in terms of b,c,m,z,p

Using Newton Raphson? (i donno how to use software, only know how to use handwritten)

phyzguy
Science Advisor
You could try Wolfram Alpha, which uses the Newton_Raphson method in the "FindRoot" function. For example, when I took the values, {b=1, c=2, z=3, m=4, p=5}, then using x for cos(theta), the equation becomes:

(-5 - 6 x + x^2 - 4 (1 - x^2))^2 == (-4 + 4 x)^2 (1 - x^2)

Wolfram Alpha, using the link below, finds x = -.45969. you can then find theta using the arccos function, or a calculator.

http://www.wolframalpha.com/input/?...-4+(1-x^2))^2+==+(-4+4+x)^2(1-x^2),+{x,+0.5}]