Trigonometry 7th Edition

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

Chapter 2 - Section 2.1 - Definition II: Right Triangle Trigonometry - 2.1 Problem Set: 14

Answer

Required trigonometric functions are- $\sin A = \frac{2}{\sqrt 5}$ $\\csc A = \frac{\sqrt 5}{2}$ $\\cos A =\frac{1}{\sqrt 5}$ $\\sec A = \sqrt 5$ $\\tan A = 2$ $\\\cot A= \frac{1}{2}$

Work Step by Step

Steps to Answer- With the help of given diagram of triangle ABC, we will use the given information and Pythagoras Theorem to solve for 'c'- $c^{2} =a^{2} + b^{2}$ ( Pythagoras Theorem) $c^{2} = 1^{2} + 2^{2}$ $c^{2} =1+ 4$ $c^{2} = 5$ therefore $ c = \sqrt 5$ Now we can write the required six T-functions of A using a = 2, b = 1 and $c= \sqrt5$ $\sin A = \frac{a}{c} = \frac{2}{\sqrt 5}$ $\\csc A = \frac{c}{a} = \frac{\sqrt 5}{2}$ $\\cos A = \frac{b}{c} =\frac{1}{\sqrt 5}$ $\\sec A = \frac{c}{b} = \frac{\sqrt 5}{1}$ = $ \sqrt 5$ $\\tan A = \frac{a}{b} = \frac{2}{1}$ = 2 $\\\cot A = \frac{b}{a} = \frac{1}{2}$
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