Results 1 to 3 of 3

Math Help - Solving Trigonometric Equations

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    77

    Solving Trigonometric Equations

    Given that sinx = 1/2, cos x = (rt.3)/2 and 0 degrees less than or equal x less than or equal 360 degrees,
    a) Find the values of x
    b) write down the exact value of tan x.

    My solution is...
    a) x = 30, 150, 330
    but the book only says that 30 degrees is the solution... am I right? or is the book right?

    b) I have two exact values for tanx: 1/(rt.3) and -1/(rt.3)
    but the book has it down as: (rt.3)/3

    Are my answers correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    311
    Thanks
    2
    Quote Originally Posted by bhuang View Post
    Given that sinx = 1/2, cos x = (rt.3)/2 and 0 degrees less than or equal x less than or equal 360 degrees,
    a) Find the values of x
    b) write down the exact value of tan x.

    My solution is...
    a) x = 30, 150, 330
    but the book only says that 30 degrees is the solution... am I right? or is the book right?

    b) I have two exact values for tanx: 1/(rt.3) and -1/(rt.3)
    but the book has it down as: (rt.3)/3

    Are my answers correct?
    For the first one, both sin and cos are positive there will only be one solution and it will be in the first quadrant (ie 30 degrees).
    cos 150 is negative, and sin 330 is negative so are not solutions. The book is correct!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    311
    Thanks
    2
    Quote Originally Posted by Debsta View Post
    For the first one, both sin and cos are positive there will only be one solution and it will be in the first quadrant (ie 30 degrees).
    cos 150 is negative, and sin 330 is negative so are not solutions. The book is correct!
    For the second one, since tan x = sin x/cos x and bothe sin x and cos x are positive (as given) then tan x must also be positive. So the solution is 1/(rt 3). (Note that this is the same as (rt 3) /3 when the denominator is rationalised.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving trigonometric equations:
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: August 12th 2011, 11:15 AM
  2. Solving trigonometric equations
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 11th 2011, 06:20 PM
  3. Solving Trigonometric Equations
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 18th 2010, 09:10 PM
  4. Solving trigonometric equations
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: November 7th 2008, 04:45 PM
  5. Solving trigonometric equations
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: October 14th 2008, 04:53 PM

Search Tags


/mathhelpforum @mathhelpforum