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Thread: Need help with trigonometry and exact values

  1. #1
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    Need help with trigonometry and exact values

    The accute angle x radians is such that sin x = 1/4 , find the exact value of tan x
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Need help with trigonometry and exact values

    Let's start with the Pythagorean identity:

    $\displaystyle \sin^2(x)+\cos^2(x)=1$

    We are told:

    $\displaystyle \sin(x)=\frac{1}{4}$

    Can you use the above to now find $\displaystyle \cos(x)$, given that $\displaystyle x$ is an acute angle?
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    Re: Need help with trigonometry and exact values

    $$\sin x = \dfrac{\text{opp}}{\text{hyp}} = \dfrac{1}{4}$$

    $$\tan x = \dfrac{\text{opp}}{\text{adj}} = \dfrac{1}{\sqrt{4^2-1^2}}$$
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