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Q26.

Expert-verifiedFound in: Page 487

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**Trigonometric Ratios**

**Sketch a triangle that has acute angle $\mathit{\theta}$, and find the other** **five trigonometric ratios of $\mathit{\theta}$**

**$\mathit{t}\mathit{a}\mathit{n}\mathit{\theta}\mathbf{=}\sqrt{\mathbf{3}}$**

The required triangle is

The other ratios are-

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

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

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

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

Where

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

The triangle by using trigonometric ratios is-

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