I am looking to find a solution to the equation (theta-90)pi=180sin(theta)

It looks relatively unassuming at first but is giving me a significant struggle. I know how to solve it easily with graphing software or a calculator but I am looking for an elegant solution using algebra.

jboy314 Jun 24, 2014

#1**+5 **

Do we assume that theta is in degrees? If so this becomes

(θ*180/pi - 90)*pi = 180*sin(θ)

or (θ - pi/2) = sin(θ)

where θ is in radians.

However, there is no elegant algebraic solution here. Use a numerical method, such as Newton-Raphson or simple repeated substitution (say θ_{0} = 1, θ_{n} = sin(θ_{n-1}) + pi/2).

Alan Jun 24, 2014

#1**+5 **

Best Answer

Do we assume that theta is in degrees? If so this becomes

(θ*180/pi - 90)*pi = 180*sin(θ)

or (θ - pi/2) = sin(θ)

where θ is in radians.

However, there is no elegant algebraic solution here. Use a numerical method, such as Newton-Raphson or simple repeated substitution (say θ_{0} = 1, θ_{n} = sin(θ_{n-1}) + pi/2).

Alan Jun 24, 2014