Results 1 to 2 of 2

Math Help - Exact values of...

  1. #1
    Newbie Silvahere's Avatar
    Joined
    Nov 2009
    From
    California
    Posts
    7

    Exact values of...

    Find the exact values of sin2u and cos \frac{u}{2}.

    a. cscu = 3, restriction: \frac{\pi}{2} < u < \pi

    b. tanu = -\frac{8}{5}, restriction: \frac{3\pi}2 < u < 2\pi

    Please solve it step by step so I can understand it too. xD
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,325
    Thanks
    1296
    Quote Originally Posted by Silvahere View Post
    Find the exact values of sin2u and cos \frac{u}{2}.

    a. cscu = 3, restriction: \frac{\pi}{2} < u < \pi
    "cosecant" is "hypotenuse over opposite side" so imagine "hypotenuse" of length 3 and "opposite side" of length 1. You can calculate the length of the "near side". Since it is in the second quadrant,that number should be negative. Now just find cos(u) and sin(u) from that triangle and use the trig identities: sin(2u)= 2sin(u)cos(u) and cos(u/2)= \pm\sqrt{1+ cos(u)}. You can get the sign from the fact that if u is in the second quadrant, u/2 is in the first quadrant.

    b. tanu = -\frac{8}{5}, restriction: \frac{3\pi}2 < u < 2\pi
    tangent is "opposite side over near side" so imagine a triangle with "opposite side" of length 8 and "near side" of length 5. You can use the Pythagorean theorem to get the length of the hypotenuse and so sin(u) and cos(u). Since u is in the fourth quadrant, sine is negative and cosine is positive. Since u is in the fourth quadrant, u/2 is in the second quadrant, where cosine is negative.

    Please solve it step by step so I can understand it too. xD
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exact Values
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 19th 2009, 07:42 AM
  2. Exact Values
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: September 2nd 2008, 03:48 PM
  3. exact values
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: June 30th 2008, 04:52 PM
  4. exact values.. sin, cos, tan, cot, csc, sec...
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 5th 2008, 01:24 PM
  5. Exact values
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: January 13th 2007, 03:50 AM

Search Tags


/mathhelpforum @mathhelpforum