## Trigonometry 7th Edition

Published by Cengage Learning

# Chapter 2 - Section 2.1 - Definition II: Right Triangle Trigonometry - 2.1 Problem Set: 18

#### Answer

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

#### Work Step by Step

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

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