Use a double-angle or half angle identity to find the exact value to solve these two problems. Please help I'm confused about how to convert CSC to sin and tan to CSC.
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Trig help
- Thread starter Netzer7
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pka
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I can help with the second: \(\displaystyle \tan(\theta)=\frac{3}{4};~\pi\le\theta\le\frac{3\pi}{2}\) find \(\displaystyle \csc(2\theta)\)
Note that \(\displaystyle \theta\in\text{Quad}III\). Thus \(\displaystyle \sin(\theta)=\frac{-3}{5}~\&~\cos(\theta)=\frac{-4}{5}\)
\(\displaystyle \begin{align*}\csc(2\theta)&=\frac{1}{\sin(2\theta)} \\&=\frac{1}{2\sin(\theta)\cos(\theta)}\\&\text{can you finish ?} \end{align*}\)
Note that \(\displaystyle \theta\in\text{Quad}III\). Thus \(\displaystyle \sin(\theta)=\frac{-3}{5}~\&~\cos(\theta)=\frac{-4}{5}\)
\(\displaystyle \begin{align*}\csc(2\theta)&=\frac{1}{\sin(2\theta)} \\&=\frac{1}{2\sin(\theta)\cos(\theta)}\\&\text{can you finish ?} \end{align*}\)