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Math Help - Finding Values of the Trig Function

  1. #1
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    Finding Values of the Trig Function

    Hello, Working on some Math Home work, and i am stuck.

    Find the value of the trig function indicated:

    6) cos θFinding Values of the Trig Function-triangle.png

    would it just be 8/17?


    No clue on this one
    Find the value of the trig function indicated:

    22) find sin θ if tan θ = 3/4
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  2. #2
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    Re: Finding Values of the Trig Function

    Quote Originally Posted by HelpMeTrigonometry View Post
    Hello, Working on some Math Home work, and i am stuck.
    Find the value of the trig function indicated:

    6) cos θClick image for larger version. 

Name:	triangle.png 
Views:	5 
Size:	13.1 KB 
ID:	23619

    would it just be 8/17?

    yes, \cos{\theta} = \frac{adjacent \, side}{hypotenuse}


    No clue on this one
    Find the value of the trig function indicated:

    22) find sin θ if tan θ = 3/4
    \tan{\theta} = \frac{opposite \, side}{adjacent \, side}

    use Pythagoras to find the hypotenuse, then ...

    \sin{\theta} = \frac{opposite \, side}{hypotenuse}
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  3. #3
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    Re: Finding Values of the Trig Function

    Quote Originally Posted by skeeter View Post
    \tan{\theta} = \frac{opposite \, side}{adjacent \, side}

    use Pythagoras to find the hypotenuse, then ...

    \sin{\theta} = \frac{opposite \, side}{hypotenuse}
    Even though your method is the simplest, it assumes that the answer is in the first quadrant, which it might not be. Once the OP has found \displaystyle \begin{align*} \tan{\theta} \end{align*} for \displaystyle \begin{align*} \theta \end{align*} in the first quadrant, he/she needs to realise that \displaystyle \begin{align*} \tan{\theta} \end{align*} is also positive in the third quadrant, and in the third quadrant, \displaystyle \begin{align*} \sin{\theta} \end{align*} is negative.

    So there are actually two possibilities, the positive and the negative of what the OP finds using your method
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  4. #4
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    Re: Finding Values of the Trig Function

    Quote Originally Posted by Prove It View Post
    Even though your method is the simplest, it assumes that the answer is in the first quadrant, which it might not be. Once the OP has found \displaystyle \begin{align*} \tan{\theta} \end{align*} for \displaystyle \begin{align*} \theta \end{align*} in the first quadrant, he/she needs to realise that \displaystyle \begin{align*} \tan{\theta} \end{align*} is also positive in the third quadrant, and in the third quadrant, \displaystyle \begin{align*} \sin{\theta} \end{align*} is negative.

    So there are actually two possibilities, the positive and the negative of what the OP finds using your method
    Given the level of the question (looks like basic right triangle trig) , I kept the means of solution rather simple. Why make it more difficult for someone who asks for confirmation that their cosine ratio is correct?

    I don't really believe the OP is at the level of dealing with trig functions ... yet.
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