If tan 0 = 5/12, what is sin 0?

2 answers:

7 0

Sin is 5/13

We know tan = 5/12 the 5 is opposite 12 adjacent
Sin is opposite/hypotenuse. We know 5 is the opposite to find hypotenuse do pythogrean 5^2+12^2= 169 the sq rt of 169 is 13

sveticcg [70]3 years ago

5 0

Sin = $\frac{5}{13}$

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Find the exact value of tan (arcsin (two fifths)). For full credit, explain your reasoning.

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$\bf sin^{-1}(some\ value)=\theta \impliedby \textit{this simply means}
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sin(\theta )=some\ value\qquad \textit{now, also bear in mind that}
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\qquad 
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}\\\\
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$\bf sin^{-1}\left( \frac{2}{5} \right)=\theta \impliedby \textit{this simply means that}
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sin(\theta )=\cfrac{2}{5}\cfrac{\leftarrow opposite}{\leftarrow hypotenuse}\qquad \textit{now let's find the adjacent side}
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\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad 
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c=hypotenuse\\
a=adjacent\\
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$\bf \pm \sqrt{5^2-2^2}=a\implies \pm\sqrt{21}=a
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\textit{we don't know if it's +/-, so we'll assume is the + one}\quad \sqrt{21}=a\\\\
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tan(\theta)=\cfrac{opposite}{adjacent}\qquad \qquad tan(\theta)=\cfrac{2}{\sqrt{21}}
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\textit{and now, let's rationalize the denominator}
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