Chapter 4, Problem 100RE

a.

To determine

To complete: the given table.

$\theta$	0.1	0.4	0.7	1.0	1.3
$\tan \left(\theta -\frac{\pi }{2}\right)$
$-\cot \theta$

Answer to Problem 100RE

$\theta$	0.1	0.4	0.7	1.0	1.3
$\tan \left(\theta -\frac{\pi }{2}\right)$	-9.97	-2.37	-1.19	-0.64	-0.28
$-\cot \theta$	-9.97	-2.37	-1.19	-0.64	-0.28

Explanation of Solution

First use the calculator to complete the given table:

  $\tan \left(0.1-\frac{\pi }{2}\right)=-9.97$

  $\tan \left(0.4-\frac{\pi }{2}\right)=-2.37$

  $\tan \left(0.7-\frac{\pi }{2}\right)=-1.19$

  $\tan \left(1.0-\frac{\pi }{2}\right)=-0.64$

  $\tan \left(0.1-\frac{\pi }{2}\right)=-0.28$

And

  $-\cot \left(0.1\right)=-9.97$

  $-\cot \left(0.4\right)=-2.37$

  $-\cot \left(0.7\right)=-1.19$

  $-\cot \left(1.0\right)=-0.64$

  $-\cot \left(0.1\right)=-0.28$

Thus,

$\theta$	0.1	0.4	0.7	1.0	1.3
$\tan \left(\theta -\frac{\pi }{2}\right)$	-9.97	-2.37	-1.19	-0.64	-0.28
$-\cot \theta$	-9.97	-2.37	-1.19	-0.64	-0.28

b.

To determine

To explain: the relationship between $\tan \left(\theta -\frac{\pi }{2}\right)$ and $-\cot \theta$ .

Answer to Problem 100RE

The two functions are the same.

Explanation of Solution

By observing the table obtained from part (a),

$\theta$	0.1	0.4	0.7	1.0	1.3
$\tan \left(\theta -\frac{\pi }{2}\right)$	-9.97	-2.37	-1.19	-0.64	-0.28
$-\cot \theta$	-9.97	-2.37	-1.19	-0.64	-0.28

It can be said that both the functions are the same.