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Q21.

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Precalculus Mathematics for Calculus

Found in: Page 487

Book edition 7th Edition

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

Pages 948 pages

ISBN 9781337067508

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Short Answer

Trigonometric Ratios
Express $x$ and $y$ in terms of trigonometric ratios of $θ$

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

A triangle is given with a side of 28.

Step 2. Concept used

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

$\begin{array}{l} \Rightarrow \sin θ = \frac{p e r p e n d i c u l a r}{h y p o t e n u s e} = \frac{P}{H} \\ \Rightarrow \cos θ = \frac{b a s e}{h y p o t e n u s e} = \frac{B}{H} \\ \Rightarrow \tan θ = \frac{p e r p e n d i c u l a r}{b a s e} = \frac{P}{B} \end{array}$

Step 3. Calculation

From given figure,

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

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

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