How to solve an equation with one unknown and both sine and cosine
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Michael Boyte
on 17 Jun 2022
Answered: Star Strider
on 17 Jun 2022
I am trying to solve an equation for a theta value. The theta is th eonly unknown and it appears in both a sine and a cosine function. An example of an equation I am trying to solve looks like this:
3.0179 = 6*cos(theta) - 2*sin(theta)*0.8660254038
I know that theta must equal 45 or 315 degrees. But when I use solve(), I get this answer:
-log((2989227959^(1/2) - 30179i)/(10000*(3^(1/2) - 6i)))*1i
-log(-(2989227959^(1/2) + 30179i)/(10000*(3^(1/2) - 6i)))*1i
How can I go about solving this equation for theta?
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Accepted Answer
Star Strider
on 17 Jun 2022
Try this —
syms theta
Eqn = 3.0179 == 6*cos(theta) - 2*sin(theta)*0.8660254038
theta = solve(Eqn, theta)
thetav = vpa(theta, 9)
format long
thetad = double(theta)
.
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