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# Algebraic solution to (theta-90)pi=180sin(theta)

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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.

Jun 24, 2014

### Best Answer

#1
+33566
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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 θ0 = 1, θn = sin(θn-1) + pi/2).

Jun 24, 2014

### 2+0 Answers

#1
+33566
+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 θ0 = 1, θn = sin(θn-1) + pi/2).

Alan Jun 24, 2014
#2
+576
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initially it was in degrees and it should be noted that the 180 on the right side was initially in degrees.  I'm sort of disappointed to hear that there is not an elegant way to solve this!

Jun 24, 2014