Results 1 to 5 of 5

Math Help - Finding an angle

  1. #1
    Member
    Joined
    May 2011
    Posts
    178
    Thanks
    6

    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?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    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)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2011
    Posts
    178
    Thanks
    6
    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?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by Bashyboy View Post
    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,

    \cot \theta = -.2315

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

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

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

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

    Follow Math Help Forum on Facebook and Google+

  5. #5
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by Bashyboy View Post
    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
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding the angle
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: July 12th 2010, 04:58 PM
  2. Finding angle/ Double angle formula
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: May 29th 2009, 07:43 AM
  3. Finding an angle
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 27th 2009, 08:02 PM
  4. Finding an angle
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: October 10th 2007, 04:40 PM
  5. finding the angle
    Posted in the Trigonometry Forum
    Replies: 8
    Last Post: October 30th 2006, 12:49 AM

Search Tags


/mathhelpforum @mathhelpforum