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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q 65. (page 458)

In Problem, write each trigonometric expression as an algebraic expression in $u$ .
$\tan (c o t^{- 1} u)$

Short Answer

Expert verified

Trigonometric expression $\tan (c o t^{- 1} u)$ as an algebraic expression in $u$ is given by $\frac{1}{u}$ .

Step by step solution

01

Step 1. Given information

An expression is $\tan (c o t^{- 1} u)$ .

02

Step 2. Value of the expression in terms of u.

Consider the expression $\tan (c o t^{- 1} u)$ .

Use the formula: $c o t^{- 1} u = \tan^{- 1} (\frac{1}{u})$

So,

$\begin{array}{rcl} \tan (c o t^{- 1} u) & = & \tan [\tan^{- 1} (\frac{1}{u})] \\ = & \frac{1}{u} \end{array}$

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Most popular questions from this chapter

Express the product $\sin (4 胃) \sin (2 胃)$ as a sum containing only sines or only cosines.

Establish each identity.

$\frac{\cos 胃 + \sin 胃 - \sin^{3} 胃}{\sin 胃} = c o t 胃 + \cos^{2} 胃$

True or False:

$\tan 2 胃 + \tan 2 胃 = \tan (4 胃)$

Sawtooth Curve An oscilloscope often displays a sawtooth curve. This curve can be approximated by sinusoidal curves of varying periods and amplitudes. A first approximation to the sawtooth curve is given by

$y = \frac{1}{2} \sin (2 蟺 x) + \frac{1}{4} \sin (4 蟺 x)$

Show that $y = \sin (2 蟺 x) \cos^{2} (蟺 x)$

$\tan^{2} (胃) - \sec^{2} (胃)$

See all solutions

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