1. ## Finding an angle

The question goes as follows: "Find two positive angles less than 360 deg. whose trigonometric function is given. Round angles to a tenth of a deg." I am given
cot \theta \equiv -.2315. So what I do is I find the reciprocal of that number to allow me to use the tan inverse function. After that, I am left with -77 deg. Well it is pretty explicit that -77 deg. is not a positive angle, so, I surmise then that +77 deg is a positive angle in the first quadrant wherein the tan/cot is positive; I also know that the tan/cot is positive in the third, so then I add 77 deg. to 180 deg and come up with 257 deg. So in my mind, I believe the two angles to be 77 and 257 deg--yet, as I turn the pages so confidently to the answer key, I find answers to be: 103 and 283 deg. Why is this so?

2. None of those answers are right - you need ONE number after the decimal point.

Neither cot(x) nor tan(x) are reflected in the y axis so you can't simply change the sign. Instead use the fact that both graphs are periodic and repeat themselves every 180 degrees (ie: cot(x) = cot(x+180) for any x in the domain)

3. So then the answers 103 and 283 deg., the ones in the answer key, are wrong? (Which would make sense because this textbook is infamous for its errors). So then what would the correct answers be?

4. Originally Posted by Bashyboy
The question goes as follows: "Find two positive angles less than 360 deg. whose trigonometric function is given. Round angles to a tenth of a deg." I am given
cot \theta \equiv -.2315. So what I do is I find the reciprocal of that number to allow me to use the tan inverse function. After that, I am left with -77 deg. Well it is pretty explicit that -77 deg. is not a positive angle, so, I surmise then that +77 deg is a positive angle in the first quadrant wherein the tan/cot is positive; I also know that the tan/cot is positive in the third, so then I add 77 deg. to 180 deg and come up with 257 deg. So in my mind, I believe the two angles to be 77 and 257 deg--yet, as I turn the pages so confidently to the answer key, I find answers to be: 103 and 283 deg. Why is this so?
Hi Bashyboy,

$\displaystyle \cot \theta = -.2315$

$\displaystyle \frac{1}{\cot \theta}=\frac{1}{-.2315}=\tan \theta = -4.3197$

$\displaystyle \tan^{-1}(-4.3197)=\theta=-76.97^{\circ}$

$\displaystyle -76.97^{\circ}+180^{\circ}=103.03^{\circ}$

$\displaystyle -76.97^{\circ}+360=283.03^{\circ}$

5. Originally Posted by Bashyboy
So then the answers 103 and 283 deg., the ones in the answer key, are wrong? (Which would make sense because this textbook is infamous for its errors). So then what would the correct answers be?
Almost. The correct answer is 103.0 degrees and 283.0 degrees - the trailing 0 is significant and since the question says "Round angles to a tenth of a deg" you'll lose an answer mark if you leave them out