Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 2 - Section 2.2 - Calculators and Trigonometric Functions of an Acute Angle - 2.2 Problem Set - Page 72: 78

Answer

$\tan 10^{\circ} 30'$ = $0.1853$ $\cot 79^{\circ} 30'$= $0.1853$ Thus, results justify the Cofunction Theorem.

Work Step by Step

Given pair is- $\tan 10^{\circ} 30'$ , $\cot 79^{\circ} 30'$ As 60' = $1^{\circ}$, therefore 30' = $0.5^{\circ}$ Hence pair becomes- $\tan 10.5^{\circ} $ , $\cot 79.5^{\circ}$ Using reciprocal identity for $\cot$- $\tan 10.5^{\circ} $ , $\frac{1}{\tan79.5^{\circ}}$ Using calculator in degree mode- (10.5 → $\tan$) and ( 79.5 → $\tan$) $0.1853390449$ , $\frac{1}{5.3955171743}$ Now using calculator for reciprocal as required- $0.1853390449$ , $0.1853390449$ Rounding to four places past the decimal point- $0.1853$ , $0.1853$ i.e $\tan 10^{\circ} 30'$ = $0.1853$ $\cot 79^{\circ} 30'$= $0.1853$ Thus, results justify the Cofunction Theorem.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.