Results 1 to 8 of 8

Thread: Given tan (theta) what is sin (theta)

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    184

    Given tan (theta) what is sin (theta)

    if pi/2 ≤ theta ≤ 3pi/2 and tanθ = -4/3
    Determine the exact value of sinθ

    if the answer was something I could use the special triangles to solve It wouldnt be so hard ie(1/2, root3/2 ....)

    I could maybe draw it out and solve, but how do you do something like this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    9
    Quote Originally Posted by brentwoodbc View Post
    if pi/2 ≤ theta ≤ 3pi/2 and tanθ = -4/3
    Determine the exact value of sinθ

    if the answer was something I could use the special triangles to solve It wouldnt be so hard ie(1/2, root3/2 ....)

    I could maybe draw it out and solve, but how do you do something like this?
    $\displaystyle \frac{\pi}{2} \leq \theta \leq \frac{3 \pi}{2}$ means that you're in either the 2nd or 3rd quadrant. But tan is negative in the 3rd quadrant and the 4th quadrant. Therefore $\displaystyle \theta$ lies in the second quadrant.

    Now draw a right-triangle with angle $\displaystyle \theta$ such that the opposite side is 4 and the adjacent side is 3. Clearly the hypotenuse is 5. Then $\displaystyle \sin \theta = \frac{4}{5}$ (because sine is positive in the 2nd quadrant).
    Last edited by mr fantastic; Jun 5th 2009 at 07:24 PM. Reason: Fixed a careless mistake
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2008
    Posts
    184
    how do you know what quadrant it is in? how do you get theta from the triangle?
    Last edited by mr fantastic; Jun 5th 2009 at 07:28 PM. Reason: Edited because of an earlier mistake I made.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    9
    Quote Originally Posted by brentwoodbc View Post
    Thank you.

    + or - ? answers given are

    -4/5

    -3/5

    3/5

    4/5
    I edited my original post because I made a careless mistake.

    Quote Originally Posted by brentwoodbc View Post
    [snip] how do you get theta from the triangle?
    Use basic trigonometry to get the magnitude of $\displaystyle \sin \theta$. Then decide whether it's plus or minus.
    Last edited by mr fantastic; Jun 5th 2009 at 07:26 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2008
    Posts
    184
    Im not allowed a calc. so how else would I find if it's plus/ neg.
    Last edited by mr fantastic; Jun 5th 2009 at 07:26 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    9
    Quote Originally Posted by brentwoodbc View Post
    [snip]
    Im not allowed a calc. so how else would I find if it's plus/ neg.
    I assume that you're expected to be familiar with how the definition of sine (and cosine) relates to the unit circle. That's why I have refered to quadrants. You're expected to know what the sign of sine (and cosine) and tan is in each quadrant.
    Last edited by mr fantastic; Jun 5th 2009 at 07:27 PM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Nov 2008
    Posts
    184
    Quote Originally Posted by mr fantastic View Post
    $\displaystyle \frac{\pi}{2} \leq \theta \leq \frac{3 \pi}{2}$ means that you're in either the 2nd or 3rd quadrant. But tan is negative in the 3rd quadrant and the 4th quadrant. Therefore $\displaystyle \theta$ lies in the second quadrant.

    Now draw a right-triangle with angle $\displaystyle \theta$ such that the opposite side is 4 and the adjacent side is 3. Clearly the hypotenuse is 5. Then $\displaystyle \sin \theta = \frac{4}{5}$ (because sine is positive in the 2nd quadrant).
    thanks that makes more sense, but isnt tan supposed to be negative?
    (tan(theta)=-4/3)
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    9
    Quote Originally Posted by brentwoodbc View Post
    thanks that makes more sense, but isnt tan supposed to be negative?
    (tan(theta)=-4/3)
    In the second quadrant tan is negative and sine is positive. The triangle I used earlier gives you the size of $\displaystyle \sin \theta$. Then you examine the quadrant the angle is in to decide whether the answer is +ve or -ve.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: Apr 29th 2010, 09:24 AM
  2. Replies: 2
    Last Post: Mar 29th 2010, 06:38 AM
  3. Replies: 3
    Last Post: Feb 6th 2009, 03:19 PM
  4. Replies: 1
    Last Post: Jan 23rd 2009, 09:53 AM
  5. Solve sin4(theta) = cos2(theta)
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Dec 8th 2008, 10:23 AM

Search Tags


/mathhelpforum @mathhelpforum