Results 1 to 3 of 3

Math Help - trigo>find angle

  1. #1
    Junior Member
    Joined
    Sep 2008
    From
    Australia
    Posts
    72

    trigo>find angle

    cos(A-30*)=3cos(A+30*)

    how to do???i stuck at beginning.

    THX FOR WHO HELP~
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Aug 2008
    Posts
    530
    Quote Originally Posted by sanikui View Post
    cos(A-30*)=3cos(A+30*)

    how to do???i stuck at beginning.

    THX FOR WHO HELP~
    Do you know these formulae:

    cos (A + B)= cosA cosB - sinA sinB

    cos (A - B) = cosA cosB + sinA sinB

    Now apply these formulae and see here,

    cos (A - 30) = 3 cos (A + 30)

    \Rightarrow cosA cos30 + sinA sin30 = 3(cosA cos30 - sinA sin30)

    \Rightarrow cosA cos30 + sinA sin30 - 3cosA cos30 - 3sinA sin30 = 0

    \Rightarrow -2cosA cos30 + 4sinA sin30 = 0

    \Rightarrow -2cosA \left(\frac{\sqrt{3}}{2}\right) + 4sinA \left(\frac{1}{2}\right) = 0

    \Rightarrow -\sqrt{3} \;cosA  + 2sinA = 0

    \Rightarrow 2sinA = \sqrt{3} \;cosA

    \Rightarrow \frac {sinA}{cosA} = \frac{\sqrt{3}}{2}

    \Rightarrow tanA = \frac{\sqrt{3}}{2}

    \Rightarrow tanA = 0.866

    A = 41\;\;degrees
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2008
    From
    Australia
    Posts
    72
    Quote Originally Posted by Shyam View Post
    Do you know these formulae:

    cos (A + B)= cosA cosB - sinA sinB

    cos (A - B) = cosA cosB + sinA sinB

    Now apply these formulae and see here,

    cos (A - 30) = 3 cos (A + 30)

    \Rightarrow cosA cos30 + sinA sin30 = 3(cosA cos30 - sinA sin30)

    \Rightarrow cosA cos30 + sinA sin30 - 3cosA cos30 - 3sinA sin30 = 0

    \Rightarrow -2cosA cos30 + 4sinA sin30 = 0

    \Rightarrow -2cosA \left(\frac{\sqrt{3}}{2}\right) + 4sinA \left(\frac{1}{2}\right) = 0

    \Rightarrow -\sqrt{3} \;cosA  + 2sinA = 0

    \Rightarrow 2sinA = \sqrt{3} \;cosA

    \Rightarrow \frac {sinA}{cosA} = \frac{\sqrt{3}}{2}

    \Rightarrow tanA = \frac{\sqrt{3}}{2}

    \Rightarrow tanA = 0.866

    A = 41\;\;degrees
    Yes, the answer is right. But the answer got 2 angles. Becouse tangent positive in 1st and 3rd quadrant.
    A=41* and 221*
    thx thx V^^
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 4th 2011, 11:36 AM
  2. Replies: 3
    Last Post: April 16th 2009, 08:45 AM
  3. Find>trigo~!
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: September 16th 2008, 08:39 PM
  4. trigo>angle
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: September 11th 2008, 10:28 PM
  5. find trigo ratio
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: February 12th 2008, 03:08 AM

Search Tags


/mathhelpforum @mathhelpforum