Chapter 2, Problem 1RE

Find exact values of the six trigonometric functions for each angle A.

To determine

The six trigonometric functions for angle $A$ if the figure of triangle:

Answer to Problem 1RE

Solution: The six trigonometric functions are

$\sin A=\frac{60}{61},\cos A=\frac{11}{61},\tan A=\frac{60}{11},\mathrm{cosec}A=\frac{61}{60},\sec A=\frac{61}{11},\cot A=\frac{11}{60}$

Given: The figure of triangle:

Explanation of Solution

Consider the given triangle:

Substitute the adequate values below to get all trigonometric functions:

$\begin{array}{c}\sin A=\frac{\text{side opposite to }A}{\text{hypotenuse}}\\ =\frac{60}{61}\\ \cos A=\frac{\text{side adjacent to }A}{\text{hypotenuse}}\\ =\frac{11}{61}\end{array}$

$\begin{array}{c}\tan A=\frac{\text{side opposite to }A}{\text{side adjacent to }A}\\ =\frac{60}{11}\\ \mathrm{cosec}A=\frac{\text{hypotenuse}}{\text{side opposite to }A}\\ =\frac{61}{60}\end{array}$

$\begin{array}{c}\sec A=\frac{\text{hypotenuse}}{\text{side adjacent to }A}\\ =\frac{61}{11}\\ \cot A=\frac{\text{side adjacent to }A}{\text{side opposite to }A}\\ =\frac{11}{60}\end{array}$

The six trigonometric functions are

$\sin A=\frac{60}{61},\cos A=\frac{11}{61},\tan A=\frac{60}{11},\mathrm{cosec}A=\frac{61}{60},\sec A=\frac{61}{11},\cot A=\frac{11}{60}$.