My Math Forum different values from different ratios

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 January 12th, 2014, 03:39 PM #1 Newbie   Joined: Jan 2014 Posts: 2 Thanks: 0 different values from different ratios I have the sine ratio of 5/root of 61, the cosine ratio of -6/root of 61and the tangent ratio of -5 over 6. I need to find the angle in degrees. To do this, I use inverse sin/cos/tan do I not? Because when I do inverse cos I get the correct answer of 140.2, but when using inverse sin and tan I get 39.8. Why is this and how do I know which inverse to use?
 January 12th, 2014, 03:51 PM #2 Newbie   Joined: Jan 2014 Posts: 2 Thanks: 0 Re: different values from different ratios These values are based off of the point -6,5 and these ratios are correct.
 January 13th, 2014, 12:31 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,627 Thanks: 2077 When you use inverse tan, you don't get 39.8. You get -39.8. The points (-6, 5) and (6, -5) both require evaluation of the inverse tangent of -5/6, so the result given by your calculator can't be correct for both. To obtain the correct result from the value given by your calculator, you need to be aware of the signs of the coordinates as well as their values and ratio. I'm sure you can figure out the correct procedure for each quadrant and for points that lie on one of the axes.

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