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Expert-verified Found in: Page 487 ### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508 # Trigonometric RatiosSketch a triangle that has acute angle $\mathbit{\theta }$, and find the other five trigonometric ratios of $\mathbit{\theta }$$\mathbit{t}\mathbit{a}\mathbit{n}\mathbit{\theta }\mathbf{=}\sqrt{\mathbf{3}}$

The required triangle is The other ratios are-

$\begin{array}{l}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{\theta }\mathbf{=}\frac{\sqrt{\mathbf{3}}}{\mathbf{2}}\\ \mathbf{c}\mathbf{o}\mathbf{s}\mathbf{\theta }\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\\ \mathbf{c}\mathbf{s}\mathbf{c}\mathbf{\theta }\mathbf{=}\frac{\mathbf{2}}{\sqrt{\mathbf{3}}}\\ \mathbf{s}\mathbf{e}\mathbf{c}\mathbf{\theta }\mathbf{=}\mathbf{2}\\ \mathbf{c}\mathbf{o}\mathbf{t}\mathbf{\theta }\mathbf{=}\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}\end{array}$

See the step by step solution

## Step 1. Given information

A trigonometric ratio is given as $\mathrm{tan}\theta =\sqrt{3}$.

## Step 2. Concept used

To begin, locate the triangle's unknown side. Then, using the following trigonometric ratios, draw the triangle-

$\begin{array}{l}⇒\mathrm{sin}\theta =\frac{p}{h}&\mathrm{csc}\theta =\frac{h}{p}\\ ⇒\mathrm{cos}\theta =\frac{b}{h}&\mathrm{sec}\theta =\frac{h}{b}\\ ⇒\mathrm{tan}\theta =\frac{p}{b}&\mathrm{cot}\theta =\frac{b}{p}\end{array}$

Where

$\begin{array}{l}h=hypotenuse\\ b=base\\ p=perpendicular\end{array}$

## Step 3. Calculation

The triangle by using trigonometric ratios is-  ### Want to see more solutions like these? 