Results 1 to 6 of 6

Math Help - Prove d/dθ(sinθ) = pie/180cosθ (chain rule)

  1. #1
    Banned
    Joined
    Apr 2010
    Posts
    58

    Prove d/dθ(sinθ) = pie/180cosθ (chain rule)

    Use the Chain Rule to show that if θ is measured in degrees, then:

    d/dθ(sinθ) = pie/180cosθ

    I could only derive the left side to cosθ, but had no clue what to do with the right side.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Apr 2010
    Posts
    59
    well then you have:

    cosθ = pie / 180cosθ

    180cosθ = pie / cosθ

    180cosēθ = pie

    Basic, erm, also, you know that 180 degrees = pie as well
    Follow Math Help Forum on Facebook and Google+

  3. #3
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by TsAmE View Post
    Use the Chain Rule to show that if θ is measured in degrees, then:

    d/dθ(sinθ) = pie/180cosθ

    I could only derive the left side to cosθ, but had no clue what to do with the right side.
    It is because \theta ^{\circ} = \frac{\pi}{180} \theta

    By the chain rule (for a constant a): \frac{d}{d \theta}\, \sin (a \theta) = a\cos(a \theta)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Apr 2010
    Posts
    58
    But there was no constant in the question? And wouldnt you only work with the left hand side-d/dθ(sinθ), to get to (pie / 180) * cosθ since you are kind of proving the left hand side? Sorry but I am kind of confused
    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 TsAmE View Post
    But there was no constant in the question? And wouldnt you only work with the left hand side-d/dθ(sinθ), to get to (pie / 180) * cosθ since you are kind of proving the left hand side? Sorry but I am kind of confused
    You want to manipulate the left side to get the right side

    You are given theta in degrees and since \frac{d}{dx} \sin(x) = \cos(x)<br />
only holds in radians then you need to convert degrees to radians.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Banned
    Joined
    Apr 2010
    Posts
    58
    Ok that makes more sense, but by differentiating the LHS, it seems that chain rule wasn't used, and just the trig derivative, yet the question said prove using chain rule. Sorry again if I am asking a dumb question
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Use The Chain Rule To Prove f+g is Differentiable
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: June 19th 2010, 07:21 AM
  2. Chain Rule Inside of Chain Rule
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 22nd 2009, 08:50 PM
  3. Replies: 5
    Last Post: October 19th 2009, 01:04 PM
  4. Replies: 3
    Last Post: May 25th 2009, 06:15 AM
  5. Replies: 2
    Last Post: December 13th 2007, 05:14 AM

Search Tags


/mathhelpforum @mathhelpforum