Results 1 to 5 of 5

Math Help - Graphs of Sine and Cosine

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    51

    Graphs of Sine and Cosine

    Hello again!

    Using a weight on a string called a plumb bob, it is possible to erect a pole that is exactly vertical, which means that the pole points directly toward the center of the earth. Two such poles are erected one hundred miles apart. If the the poles were extended they would meet at the center of the earth at an angle of 1.4333^o. Compare the radius of the earth.

    So that's the question and I'm just totally lost because I cant seem to picture it.

    The equation for Arc length is S = r\theta

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Nov 2009
    Posts
    49
    Hello again!

    Using a weight on a string called a plumb bob, it is possible to erect a pole that is exactly vertical, which means that the pole points directly toward the center of the earth. Two such poles are erected one hundred miles apart. If the the poles were extended they would meet at the center of the earth at an angle of . Compare the radius of the earth.

    So that's the question and I'm just totally lost because I cant seem to picture it.

    The equation for Arc length is

    Thanks!

    ------------------------------------------------------------------

    basically imagine two poles that meet at the center of the earth, on the surface the poles are a distance of 100miles away but it is a slightly curved path as the earth is naturally curved, we will call this distance S for arc length. S=100, Q(theta)= 43/30 and we need r. well? this is a straightfoward solution. using s=rq. r=s/q. r=100/43/30. r=3000/43.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2009
    Posts
    51
    Quote Originally Posted by purebladeknight View Post

    basically imagine two poles that meet at the center of the earth, on the surface the poles are a distance of 100miles away but it is a slightly curved path as the earth is naturally curved, we will call this distance S for arc length. S=100, Q(theta)= 43/30 and we need r. well? this is a straightfoward solution. using s=rq. r=s/q. r=100/43/30. r=3000/43.

    Awesome! Thanks!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,413
    Thanks
    1852
    Unfortunately, purebladeknight's argument is incorrect. The radius of the earth is considerably larger than 3000/43= 70 miles. If it were that radius, the circumference of the earth would be 140\pi= 438 miles and you could drive around the earth in about 6 hours!

    The "equation for arclength is S= r\theta" only if [itex]\theta[/itex] is given in radians! So you need to start writing the angle in radians. 180 degrees corresponds to \pi radians so 1.4333^o degrees corresponds to 1.4333/180= 0.0079611\pi= 0.025016 radians.

    And a radian is defined so 1 radian cuts an arc equal to the radius. Here the arc is 100 miles= 0.025016 times the radius of the earth so the earth's radius is 100/0.025016= 3997 miles, approximately.

    If you wanted to do this in degrees, you could argue by proportions. An entire arc of 360^o covers the entire circumference, 2\pi r and angle of 1.4333^o covers \frac{1.4333}{360}(2\pi r) of the circumference. So we have \frac{1.4333}{360}(2\pi r)= 100 to solve for r. The first thing you would do, of course, if find that coefficient: [tex]\frac{1.4333}{360}(2\pi)= 0.025016[tex] (the radian measure we got before). Now your equation is 0.0250156 r= 100 so r= \frac{100}{0.0250156}= 3997 miles, again.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2009
    Posts
    49
    Quote Originally Posted by HallsofIvy View Post
    Unfortunately, purebladeknight's argument is incorrect. The radius of the earth is considerably larger than 3000/43= 70 miles. If it were that radius, the circumference of the earth would be 140\pi= 438 miles and you could drive around the earth in about 6 hours!

    The "equation for arclength is S= r\theta" only if [itex]\theta[/itex] is given in radians! So you need to start writing the angle in radians. 180 degrees corresponds to \pi radians so 1.4333^o degrees corresponds to 1.4333/180= 0.0079611\pi= 0.025016 radians.

    And a radian is defined so 1 radian cuts an arc equal to the radius. Here the arc is 100 miles= 0.025016 times the radius of the earth so the earth's radius is 100/0.025016= 3997 miles, approximately.

    If you wanted to do this in degrees, you could argue by proportions. An entire arc of 360^o covers the entire circumference, 2\pi r and angle of 1.4333^o covers \frac{1.4333}{360}(2\pi r) of the circumference. So we have \frac{1.4333}{360}(2\pi r)= 100 to solve for r. The first thing you would do, of course, if find that coefficient: [tex]\frac{1.4333}{360}(2\pi)= 0.025016[tex] (the radian measure we got before). Now your equation is 0.0250156 r= 100 so r= \frac{100}{0.0250156}= 3997 miles, again.
    thanks for the fix up, silly me, i never realised that the theta was in radians =p.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sine and Cosine
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: February 10th 2010, 04:33 PM
  2. Replies: 7
    Last Post: August 4th 2009, 10:14 PM
  3. when would you use cosine and sine law
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: July 31st 2008, 05:29 PM
  4. Urgent Help...Graphs of Sine and Cosine
    Posted in the Trigonometry Forum
    Replies: 22
    Last Post: November 18th 2007, 07:11 PM
  5. Sine, cosine and tan graphs
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 29th 2007, 01:47 PM

Search Tags


/mathhelpforum @mathhelpforum