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Math Help - Find the requested function value meeting all of the given conditions??

  1. #1
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    Angry Find the requested function value meeting all of the given conditions??

    I have to do this packet for an AP class I'm taking, and my teacher didn't give me anything to work with. I'm desperate.

    sin(theta)= (square root)3/2 and tan(theta) > 0 ; Find cos(theta).
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    Lightbulb Re: Find the requested function value meeting all of the given conditions??

    Darw a circle with radius=1 and center at (0,0) then on sin axis go up as much as squrt(3)/2, draw a horizontal line to intersect circle at two points...now draw tan axis and check which of the two points on circle qualifies for tan>0
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    Re: Find the requested function value meeting all of the given conditions??

    Hello, MaddyV!

    \sin\theta\,=\,\frac{\sqrt{3}}{2}\,\text{ and }\,\tan\theta > 0.\;\;\text{ Find }\,\cos\theta.

    \sin\theta is positive: . \theta is in Quadrant 1 or Quadrant 2.

    \tan\theta is positive: . \theta is in Quardrant 1 or Quadrant 3.

    . . Hence, \theta is in Quadrant 1.


    \sin\theta \:=\:\frac{\sqrt{3}}{2} \:=\:\frac{opp}{hyp}

    \theta is in a right triangle with: . opp = \sqrt{3},\;hyp = 2
    Pythagorus tell us that: . adj = 1

    Therefore: . \cos\theta \:=\:\frac{adj}{hyp} \:=\:\frac{1}{2}

    Thanks from MaddyV
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    Re: Find the requested function value meeting all of the given conditions??

    Okay, so how about:

    cos(theta) = - [(square root)2]/2 and tan(theta) < 0 ; find cot(theta) ?
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    Re: Find the requested function value meeting all of the given conditions??

    Quote Originally Posted by MaddyV View Post
    Okay, so how about:

    cos(theta) = - [(square root)2]/2 and tan(theta) < 0 ; find cot(theta) ?
    did you not learn this in your pre-AP class?

    you are expected to already know the values for sine and cosine on the unit circle and the definitions/identities for basic all six trig ratios ...

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    Re: Find the requested function value meeting all of the given conditions??

    It was actually recommended that I skip Pre-Calculus and go straight to AP Calculus AB. I was given a summer packet with these problems specifically so I could learn how to do these things.
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    Re: Find the requested function value meeting all of the given conditions??

    Why was this recommended? The only way I would recommend something like this is if you have shown that you already know how to do the topics in Pre-Calculus...
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    Re: Find the requested function value meeting all of the given conditions??

    Quote Originally Posted by MaddyV View Post
    It was actually recommended that I skip Pre-Calculus and go straight to AP Calculus AB. I was given a summer packet with these problems specifically so I could learn how to do these things.
    Whoever "recommended" this idea has set you up for failure. My advice is for you to get into a precalculus class ... now.

    Truth is, you're not ready for AP calculus.
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