Chapter 5, Problem 3RCC

a.

To determine

Show the reciprocal identities.

Answer to Problem 3RCC

The reciprocal identities are,

  $\begin{array}{l}\sec x=\frac{1}{\cos x}\\ \csc x=\frac{1}{\sin x}\\ \cot x=\frac{1}{\tan x}\end{array}$

    

Explanation of Solution

The reciprocal means flipping the numbers. At large, the reciprocal identities are identities in which the equality relation occurs by interchanging the numerator and the denominator of the number.

For example:

  $N=\frac{a}{b}$

Then the reciprocal of the N is N’,

  $N\text{'}=\frac{b}{a}$

Program:

clc
clear
close all
symsx
f=sec(x);
p=ezplot(f);
p.LineWidth=1.25;
ax=gca;
box off
set(ax,'linewidth',1.2,'fontsize',12);
ax.XAxisLocation='origin';
ax.YAxisLocation='origin';
axis tight
axis square

Query:

• Fist, we have defined the function.
• Then sketch a graph using “ezplot”.

b.

To determine

Show the Pythagorean identities.

Answer to Problem 3RCC

The Pythagorean identities are,

  $\begin{array}{l}{\cos }^2\theta +{\sin }^2\theta =1\\ {\tan }^2\theta +1={\sec }^2\theta \\ 1+{\cot }^2\theta ={\csc }^2\theta \end{array}$

Explanation of Solution

Calculation:

The Pythagorean identities are identities which are expressing the Pythagorean theorem in terms of trigonometric functions.

  $\begin{array}{l}{\cos }^2\theta +{\sin }^2\theta =1\\ {\tan }^2\theta +1={\sec }^2\theta \\ 1+{\cot }^2\theta ={\csc }^2\theta \end{array}$