Results 1 to 2 of 2

Math Help - Hi, need help on some trig funct. problems

  1. #1
    He is legend
    Guest

    Hi, need help on some trig funct. problems

    Hi I have a few problems that I need some help on:

    1. Find the point (x,y) on the unit circle that corresponds to the real number t = 4pi/3

    2. Given sin data = -2/9 and tan data > 0, find cos data.

    3. Find the reference angle for data = -155
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by He is legend View Post
    Hi I have a few problems that I need some help on:

    1. Find the point (x,y) on the unit circle that corresponds to the real number t = 4pi/3
    imagine you draw a this angle and it cuts the unit circle at a point. you can draw a right angled triangle with this point, the base of which lies on the x-axis. it will be in the 3rd quadrant, with the angle pi/3 between the angle and the negative x-axis. the hypotenuse will be 1 (the radius of the unit circle).

    using trig ratios:

    the height of the triangle (the y-value you are looking for) is given by: - sin(pi/3)

    the base (the x-value you are searching for) is given by: cos(pi/3)


    2. Given sin data = -2/9 and tan data > 0, find cos data.
    haha, there's one i never heard before! calling "theta" "data"

    note that we are in the third quadrant, since sine is negative and tangent is positive. thus, we must have a negative value for cosine as well.

    there are two ways to do this: by formula, or by trig/geometry

    by formula: note that \cos^2 \theta = 1 - \sin^2 \theta

    so, \cos \theta = \pm \sqrt{1 - \sin^2 \theta}

    as i said, here we want \cos \theta = {\color{red} - }~ \sqrt{1 - \sin^2 \theta}

    just plug in the value for the sine and simplify


    by trig/geometry. draw a right triangle. call an acute angle in the triangle \theta. since sine of this angle is 2/9 (*), label the side opposite this angle 2 and label the hypotenuse 9. you can find the adjacent side by using Pythagoras' theorem. then you know cosine = adjacent/hypotenuse (and remember to put the minus sign at the end because we are in the third quadrant).


    3. Find the reference angle for data = -155
    there's "data" again.

    write the angle as a positive one.

    -155^o = -155^o + 360^o = 205^o

    this angle is between 180 and 270. when 180 < \theta < 270, the reference angle for \theta is given by: \theta - 180. since we want the angle between \theta and the x-axis



    *) i am considering positive numbers here, we'll worry about negatives at the end. since we know what quadrant the angle is in, we know to apply a negative sign to the answer we get
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: April 15th 2010, 09:12 PM
  2. Trig Sub Problems:
    Posted in the Calculus Forum
    Replies: 5
    Last Post: February 16th 2010, 12:41 AM
  3. Find all the solutions (Inverse Trig Funct.)
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 17th 2009, 11:46 PM
  4. Continuous Funct Graph
    Posted in the Calculus Forum
    Replies: 0
    Last Post: March 2nd 2008, 09:45 AM
  5. Zeros of Cubic Poly and Inverse Funct.
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: January 19th 2008, 01:24 PM

Search Tags


/mathhelpforum @mathhelpforum