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Exact value

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  1. Jul 21, 2015 #1

    Rectifier

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    The problem

    A right triangle has an angle a and we know that ##cos \ a = \frac{1}{3}##. What is ## tan \ (90°-a) ##
    smmP7.png


    The attempt
    I know that the ration between the adjacent side and the hypothenuse is 1/3. I am not interested in the real lengths of the sides.

    I can therefore calculate the possible length of the opposite side of the angle a by applying the Pythagorean theorem.

    $$ 1^2+x^2=3^2 \\ 1+x^2=9 \\ x = \sqrt{8}= 2 \sqrt{2} $$

    I can now write out tan(a):

    $$ \tan(a)=\frac{\sqrt{8}}{1}=\sqrt{8} = 2 \sqrt{2}$$

    And here is where I get stuck :,(

    Note:
    I have to calculate the angle without any calculator.
     
  2. jcsd
  3. Jul 21, 2015 #2

    DEvens

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    Is there an angle in your problem that is equal to 90 - a? If you figure that out, then can you find the tan of that angle?
     
  4. Jul 21, 2015 #3

    Rectifier

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    Oh!
    sin(90-a)=cos(a) and cos(90-a)=sin(a)!! :D

    this means that

    $$ tan (90-a)= \frac{sin(90-a)}{cos(90-a)}= \frac{cos(a)}{sin(a)}=cot(a)$$

    Thank you so much!
     
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