Use the figures to find the exact value of the trigonometric function tan2 theta. 01510200841.png

Use the figures to find the exact value of the trigonometric function tan2 theta. 01510200841.png

Question
Trigonometric Functions
asked 2021-03-02
Use the figures to find the exact value of the trigonometric function \(\displaystyle{\tan{{2}}}\theta\). image

Answers (1)

2021-03-03
Using the triangle ,
\(\displaystyle{\tan{\theta}}=\frac{{3}}{{4}}\)
Apply the formula of the trigonometric function ,
\(\displaystyle{\tan{{2}}}\theta={\left({2}{\tan{\theta}}\right)}{\left({1}−{\tan{{2}}}\theta\right)}\)
Substitute the value of \(\displaystyle{\tan{\theta}}=\frac{{3}}{{4}}\) in the formula,
\(\displaystyle{\tan{{2}}}\theta=\frac{{{2}\cdot{\left(\frac{{3}}{{4}}\right)}}}{{{1}-{\left(\frac{{3}}{{4}}\right)}^{{2}}}}\)
Solving the equation above,
\(\displaystyle{\tan{{2}}}\theta=\frac{{\frac{{3}}{{2}}}}{{{1}-\frac{{9}}{{16}}}}\)
\(\displaystyle=\frac{{\frac{{3}}{{2}}}}{{\frac{{7}}{{16}}}}\)
\(\displaystyle=\frac{{24}}{{7}}\)
Thus the value of the trigonometric function \(\displaystyle{\tan{{2}}}\theta{i}{s}\frac{{24}}{{7}}.\)
0

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