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Find csco, cose, and tan , where is the angle shown in the figure.Give exact values, not decimal approximations.

Find csco, cose, and tan , where is the angle shown in the figure.Give exact values-example-1
User SooIn Nam
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1 Answer

13 votes
13 votes

Let 'a' represent the unknown side of the triangle.

To solve for the unknown side, we will apply the Pythagoras theorem.


a^2=b^2+c^2^{}
\begin{gathered} b=4 \\ c=5 \end{gathered}
\begin{gathered} a^2=4^2+5^2 \\ a=\sqrt[]{16+25} \\ a=\sqrt[]{41} \end{gathered}

Let solve for cscθ


\begin{gathered} \csc \theta=(1)/(\sin \theta) \\ \sin \theta=\frac{4}{\sqrt[]{41}} \\ \text{Therefore,} \\ \csc \theta=\frac{1}{\frac{4}{\sqrt[]{41}}}=\frac{\sqrt[]{41}}{4} \end{gathered}

Let us solve for cosθ


\cos \theta=\frac{5}{\sqrt[]{41}}
\begin{gathered} \frac{5}{\sqrt[]{41}} \\ \text{Rationalising} \\ \frac{5}{\sqrt[]{41}}*\frac{\sqrt[]{41}}{\sqrt[]{41}}=\frac{5\sqrt[]{41}}{41} \end{gathered}
\cos \theta=\frac{5\sqrt[]{41}}{41}

Let us solve for tanθ


\tan \theta=(4)/(5)

User Maxdow
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