Results 1 to 4 of 4

Thread: trig proof

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    62

    trig proof

    Use what you learned in calculus to show that Sin(alpha)≤alpha and sin(alpha)/cos(alpha)≥alpha holds for all 0≤alpha≤pi/2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,
    Quote Originally Posted by rmpatel5 View Post
    Use what you learned in calculus to show that Sin(alpha)≤alpha and sin(alpha)/cos(alpha)≥alpha holds for all 0≤alpha≤pi/2
    sin(alpha)≤alpha <--> sin(alpha)-alpha≤0
    Take the derivative of sin(alpha)-alpha and see its variations between 0 and pi/2

    Same goes for the other one.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2008
    Posts
    62
    Quote Originally Posted by Moo View Post
    Hello,

    sin(alpha)≤alpha <--> sin(alpha)-alpha≤0
    Take the derivative of sin(alpha)-alpha and see its variations between 0 and pi/2

    Same goes for the other one.
    I took the der. of the first one and i get cos(alpha)≤1 and the second one sec^2(x)≥1

    the first case:
    alpha goes from 0 to pi/2

    second case:
    is just alpha is 0

    i dont think my answer makes sense
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    You can use it using geometry.
    Look at the picture.
    The angle between the x-axis and the red line is $\displaystyle \alpha$.
    While the circle is a unit circle.
    Thus, the length of the arc made by $\displaystyle \alpha$ is $\displaystyle \alpha$.
    While the length of the blue line is $\displaystyle \sin \alpha$.

    Now reflect that image through the x-axis (second picture).
    We see that the length of the blue line is $\displaystyle 2\sin \alpha$.
    And the length of arc made by the blue line is $\displaystyle 2\alpha$.
    Thus, $\displaystyle 2\sin \alpha \leq 2\alpha \implies \sin \alpha \leq \alpha$.
    This is because the shortest distance between two points is a straight line.
    Attached Thumbnails Attached Thumbnails trig proof-conformal.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Trig Proof
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: Aug 28th 2010, 03:38 PM
  2. trig proof
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: May 16th 2010, 05:55 AM
  3. Trig Lab Proof
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: Feb 10th 2010, 11:11 AM
  4. Trig proof - urg
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: May 13th 2009, 06:57 AM
  5. Help with a Trig Proof
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 11th 2008, 11:16 AM

Search Tags


/mathhelpforum @mathhelpforum