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Thread: Trig Identities

  1. #1
    HMV
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    Trig Identities

    The angle is defined at quadrant 1 and it's given that tanx=(11)^(1/2)/5
    Find cosx=
    cscx=
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by HMV View Post
    The angle is defined at quadrant 1 and it's given that tanx=(11)^(1/2)/5
    Find cosx=
    cscx=
    Hi HMV,

    $\displaystyle \tan X=\frac{\sqrt{11}}{5}$

    We know that $\displaystyle tan X = \frac{y}{x}$

    That means $\displaystyle x = 5$ and $\displaystyle y = \sqrt{11}$

    Now use $\displaystyle r^2=x^2 + y^2$ to solve for r.

    Once you have values for x, y, and r you can substitute them into the following:

    $\displaystyle \cos X = \frac{x}{r}$

    $\displaystyle \csc X = \frac{r}{y}$
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  3. #3
    MHF Contributor
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    Trig Formulae

    Hello HMV
    Quote Originally Posted by HMV View Post
    The angle is defined at quadrant 1 and it's given that tanx=(11)^(1/2)/5
    Find cosx=
    cscx=
    $\displaystyle \tan x = \tfrac{\sqrt{11}}{5}$

    Since the angle is in the first quadrant, it's an acute angle. So you can draw a right-angled triangle where the opposite side to angle $\displaystyle x$ is $\displaystyle \sqrt{11}$ and the adjacent $\displaystyle = 5$.

    So the $\displaystyle \text{hypotenuse}^2 = 11 + 25 = 36$

    $\displaystyle \Rightarrow \text{hypotenuse} = 6$

    Can you complete it now?

    Grandad
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