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Q21.

Expert-verifiedFound in: Page 487

Book edition
7th Edition

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

Pages
948 pages

ISBN
9781337067508

**Trigonometric Ratios**

**Express $\mathit{x}$ and $\mathit{y}$ in terms of trigonometric ratios of $\mathit{\theta}$**

The values are $\mathit{x}\mathbf{=}\frac{\mathbf{28}}{\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{\theta}}$ and $\mathit{y}\mathbf{=}\frac{\mathbf{28}}{\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{\theta}}$

A triangle is given with a side of 28.

Only one side is given in the question. And for other sides, use trigonometric ratios as-

$\begin{array}{l}\Rightarrow \mathrm{sin}\theta =\frac{perpendicular}{hypotenuse}=\frac{P}{H}\\ \Rightarrow \mathrm{cos}\theta =\frac{base}{hypotenuse}=\frac{B}{H}\\ \Rightarrow \mathrm{tan}\theta =\frac{perpendicular}{base}=\frac{P}{B}\end{array}$

From given figure,

$\begin{array}{l}\Rightarrow \mathrm{cos}\theta =\frac{B}{H}\\ \Rightarrow \mathrm{cos}\theta =\frac{x}{28}\\ x=\frac{28}{\mathrm{cos}\theta}\end{array}$

$\begin{array}{l}\Rightarrow \mathrm{sin}\theta =\frac{P}{H}\\ \Rightarrow \mathrm{sin}\theta =\frac{y}{28}\\ y=\frac{28}{\mathrm{sin}\theta}\end{array}$

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