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 November 2nd, 2018, 10:05 PM #1 Member   Joined: Aug 2017 From: India Posts: 54 Thanks: 2 Angle conversion I calculated arc tan or inverse tan of sqrt(-3) and the result is -60. But when represented as 360 in the net it is shown as 120 Degrees. How -60 Deg is same as 120 Deg? Please advise. I know it will be something like 180 - 60 = 120. But why I should take 180 degrees and subtract 60? How that symmetry is coming? Last edited by skipjack; November 2nd, 2018 at 11:45 PM. November 2nd, 2018, 10:53 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,584 Thanks: 1430 \begin{align*} &\tan(120^\circ) = \\ &\tan(-60^\circ + 180^\circ) = \\ &\dfrac{\sin(-60^\circ+180^\circ)}{\cos(-60^\circ + 180^\circ)} = \\ &\dfrac{\sin(-60^\circ)\cos(180^\circ)+\cos(-60^\circ)\sin(180^\circ)} {\cos(-60^\circ)\cos(180^\circ)-\sin(-60^\circ)\sin(180^\circ)} = \\ &\dfrac{-\sin(-60^\circ)}{-\cos(-60^\circ)} =\\ &\dfrac{\sin(-60^\circ)}{\cos(-60^\circ)} = \\ &\tan(-60^\circ) \end{align*} November 2nd, 2018, 11:45 PM   #3
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Quote:
 Originally Posted by MathsLearner123 . . . when represented as 360 in the net . . .
What does "360 in the net" mean? November 3rd, 2018, 09:05 AM   #4
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 Originally Posted by skipjack What does "360 in the net" mean?
an online solution?

in the "internet" ? November 3rd, 2018, 10:25 AM #5 Global Moderator   Joined: Dec 2006 Posts: 21,028 Thanks: 2259 Perhaps, but I tried it on some websites and they got it right. November 3rd, 2018, 10:32 AM #6 Senior Member   Joined: Sep 2015 From: USA Posts: 2,584 Thanks: 1430 Basically the idea is that that the tangent is the ratio of the sine and cosine functions and will remain the same if the signs of both of those are flipped. $\sin(\theta) = -\sin(\theta + 180^\circ)$ $\cos(\theta) = -\cos(\theta + 180^\circ)$ and thus $\tan(\theta) = \tan(\theta + 180^\circ)$ In order to convert from a domain of say $(-180^\circ, 180^\circ]$ to $[0, 360)$ we simply add $180^\circ$ to the angle. In this case $-60^\circ + 180^\circ = 120^\circ$ Thanks from MathsLearner123 November 3rd, 2018, 10:43 AM #7 Global Moderator   Joined: Dec 2006 Posts: 21,028 Thanks: 2259 It's easier to understand by considering the geometric definition of tan. Thanks from greg1313 November 3rd, 2018, 05:18 PM   #8
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Quote:
 Originally Posted by skipjack It's easier to understand by considering the geometric definition of tan.
Can you please explain me the method ? November 4th, 2018, 02:56 AM #9 Global Moderator   Joined: Dec 2006 Posts: 21,028 Thanks: 2259 ThetaCircle.PNG If, in the above diagram, x is non-zero, tan(θ) = y/x. If the point (x, y) is moved to a different position on the circumference of the circle, so that its coordinates become (-x, -y), the ratio of those coordinates is unchanged. The point's movement can be thought of as due to a rotation of the triangle through ±180$^\circ$, so that the angle θ becomes θ ± 180$^\circ$. The tangent of the angle is unchanged, i.e. y/x = tan(θ) = tan(θ ± 180$^\circ$). Thanks from MathsLearner123 Tags angle, conversion Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post GIjoefan1976 Algebra 4 February 16th, 2016 12:55 PM Gyiove Algebra 1 February 26th, 2014 04:57 PM jake6390 Algebra 1 August 26th, 2013 07:13 AM Denegen Physics 0 May 22nd, 2012 09:57 PM Lpitt56 Algebra 5 February 29th, 2012 06:28 AM

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