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Math Help - more trigonometry i dont think anyon can answer this one its to hard.

  1. #1
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    more trigonometry i dont think anyon can answer this one its to hard.

    find the value of the other trig functions if sin vada =-2/3 and cos vada is greater than 0
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Dave1234 View Post
    find the value of the other trig functions if sin vada =-2/3 and cos vada is greater than 0
    if you think no one can answer it, why did you ask?

    you can do this by identities, or using triangles. lets use identities here.

    you should know that \sin^2 \theta + \cos^2 \theta = 1

    you know the value of \sin \theta, so plug it in and solve for \cos \theta. you will get two answers, a negative one and a positive one, but they want the positive, since they said \cos \theta > 0


    to do it by triangles, you can remember that sine = opposite/hypotenuse. so you can draw a right-triangle, with an acute angle \theta with the opposite side having a length of 2 and the hypotenuse having a length of 3. then you can use Pythagoras' theorem to find the length of the adjacent side. now cosine = adjacent/hypotenuse. just plug in the values you found



    By the way, it is "theta" not "vada"
    Last edited by Jhevon; July 4th 2008 at 12:25 PM. Reason: corrected spelling error...hope there are no more :p
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  3. #3
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    JHevon, you can use pythagorean identities. Or you can use the pythagorean theorem from which the identities are derived.

    You got \sin{\theta} = -\frac{2}{3}, and hopefully you know that \sin{\theta} = \frac{opposite\ side}{hypotenuse} = \frac{y}{r}.

    So, y = -2 and r = 3. Now replace in the pythagorean theorem and find x. Like JHevon said, when you take the square root of a number, you only count the positive root since you need cos(theta) > 0.

    After finding x, replace:
    \cos{\theta} = \frac{x}{r}
    Last edited by Chop Suey; July 8th 2008 at 12:02 PM.
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