Results 1 to 3 of 3

Math Help - Finding the x of a sine equation!

  1. #1
    Newbie
    Joined
    Feb 2008
    Posts
    6

    Exclamation Finding the x of a sine equation!

    20 = 8sin((pi/6)(x+2))+16 ........... subtract 16
    4 = 8sin(pi/6x+pi/3) ................ divide by 8
    1/2 = sin(pi/6x+pi/3) ..............arcsin1/2 to get rid of sin and get pi/6
    pi/6 = pi/6x+pi/3 .......... subtract pi/3
    -pi/6 = pi/6x ....... divide by pi/6 to get x
    -1 = x

    My question is: Is there any way to find out the other value of 1/2 sine except looking at the unit circle, which is 5pi/6?

    1/2 = sin(pi/6x+pi/3) .. arcsin1/2 to get rid of sin and get 5pi/6
    5pi/6 = pi/6x+pi/3 ... subtract pi/3
    pi/2 = pi/6x ....... divide by pi/6 to get x
    3 = x

    And, how would I do it if the y value is 10?

    10 = 8sin((pi/6)(x+2))+16

    I don't know how to go through the steps to find the one of the values for sine -3/4 (after you go through the steps)
    The only one I found was 8.3803207 for x.

    By tracing the sine graph on my calculator, I was able to get the answers 5.6196793 and 8.3803207
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,547
    Thanks
    539
    Hello, dayoung!

    I would solve it like this . . .


    We are given: . 8\sin\left[\frac{\pi}{6}(x+2)\right]+16 \:=\:20

    Subtract 16: . 8\sin\left[\frac{\pi}{6}(x+2)\right] \:=\:4

    Divide by 8: . \sin\left[\frac{\pi}{6}(x+2)\right] \:=\:\frac{1}{2}

    Take arcsine: . \frac{\pi}{6}(x+2) \:=\;\begin{Bmatrix}\frac{\pi}{6} + 2\pi n \\ \frac{5\pi}{6} + 2\pi n \end{Bmatrix}\quad\text{ for any integer }n

    Multiply by \frac{6}{\pi}\!:\;\;x + 2 \;=\;\begin{Bmatrix}1 + 12n \\ 5 + 12n \end{Bmatrix}

    Subtract 2: . x \;=\;\begin{Bmatrix}\text{-}1 + 12n \\ 3 + 12n \end{Bmatrix}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2008
    Posts
    6
    How would I do it if the y value is 10?

    10 = 8sin((pi/6)(x+2))+16

    I don't know how to go through the steps to find the one of the values for sine -3/4 (after you go through the steps)
    The only one I found was 8.3803207 for x.

    By tracing the sine graph on my calculator, I was able to get the answers 5.6196793 and 8.3803207
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding the equation of a sine function
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 18th 2011, 09:24 AM
  2. Help in Finding the Fourier Sine Transform
    Posted in the Advanced Applied Math Forum
    Replies: 6
    Last Post: August 27th 2011, 09:35 AM
  3. finding sine, cosine, and tangent of theta
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 8th 2011, 12:51 PM
  4. Finding the period of a trigonmetic sine curve
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: September 25th 2009, 03:27 PM
  5. Finding area and angles with sine ratio
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: August 16th 2008, 06:42 AM

Search Tags


/mathhelpforum @mathhelpforum