I have a problem in a solids course about mohrs circle and its principal forces. I have solved to its last part and it all checks up when putting the right angle theta which makes the shear stresses zero(61.87) but something weird happens when i pull arctan. Do come to that answer numerically. EX
For the last part i have that $\tan(2\theta) = \dfrac{20 \cdot 2}{60 - 86.6}$.
When you put in the known angle for theta they are practically the same answers. Next step is naturally to do arctan to get to theta.
$2\theta = \arctan\left(\dfrac{20\cdot2}{60-86.717}\right)$ here is the answer supposed to be $123.7$ for the right hand equation instead i get $-56$. What is going wrong? ¨ I have checked with degrees and radian.\ Theta will be 61.87. i know that angle from approximation and website http://www.jnovy.com/jnovy/calcs/MohrsCircle2d/mohrsCircle2d.html where sigmax is 60 sigmay is 86.717 and tau is 20
Calculators are programmed to return inverse trig functions only in a given range:
For $\arcsin x= \theta$, $[-90 \leq \theta \leq 90]$ (Right half of the unit circle. $\sin \theta = \sin(180 - \theta)$)
For $\arccos x = \theta$, $[-180 \leq \theta \leq 180]$ (The top half of the unit circle. $\cos \theta = \cos (-\theta)$)
For $\arctan x = \theta$, $[-90 \leq \theta \leq 90]$ (The right half of the unit circle. $\tan \theta = \tan (\theta + 180)$)
If you got $\arctan x = -56$, the other angles are: