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Q.9

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Found in: Page 473

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Rewrite in terms of sine and cosine functions: $\mathrm{tan}\left(\theta \right)csc\left(\theta \right)$

In terms of sine and cosine function we get,

$\frac{1}{\mathrm{cos}\theta }$

See the step by step solution

## Step 1: Given information

We are given an trigonometric function as $\mathrm{tan}\left(\theta \right)c\mathrm{sc}\left(\theta \right)$

## Step 2: We use trigonometric formulastan(θ)=sinθcosθcscθ=1sinθ

We get,

$\mathrm{tan}\left(\theta \right)c\mathrm{sc}\left(\theta \right)\phantom{\rule{0ex}{0ex}}=\frac{\mathrm{sin}\left(\theta \right)}{\mathrm{cos}\left(\theta \right)}\frac{1}{\mathrm{sin}\left(\theta \right)}\phantom{\rule{0ex}{0ex}}=\frac{1}{\mathrm{cos}\left(\theta \right)}\phantom{\rule{0ex}{0ex}}=sec\theta$

## Step 3: Conclusion

The function in terms of sine and cosine can be given as $\frac{1}{\mathrm{cos}\theta }$