/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 106 Explain why tan \(90^{\circ}\) i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 106

Explain why tan \(90^{\circ}\) is undefined.

Short Answer

Expert verified
The tangent of \(90^{\circ}\) is undefined because it results in a division by zero scenario, which is undefined in mathematics.

Step by step solution

01

Understanding the Tangent Function

The tangent function, abbreviated as tan, in trigonometry is the ratio of the sine to the cosine of an angle. That is, \(\text{tan} (\theta) = \frac{\text{sin} (\theta)}{\text{cos} (\theta)}\), where \(\theta\) represents an angle.
02

Evaluation of Sine and Cosine

Firstly, evaluate the sine and cosine for \(90^{\circ}\). From the unit circle, we find that \(\text{sin} (90^{\circ}) = 1\) and \(\text{cos} (90^{\circ}) = 0\).
03

Substitution into the Tangent Function

Substitute these values into the formula for the tangent, \(\text{tan} (\theta) = \frac{\text{sin} (\theta)}{\text{cos} (\theta)}\). Resulting in: \(\text{tan} (90^{\circ}) = \frac{1}{0}\).
04

Explanation of the Undefined Result

Division by zero is undefined in mathematics because there is no number that can multiply by zero to give a non-zero number. Hence the tangent of \(90^{\circ}\) is undefined.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use a right triangle to write each expression as an algebraic expression. Assume that \(x\) is positive and that the given inverse trigonometric function is defined for the expression in \(x\). $$ \sec \left(\sin ^{-1} \frac{x}{\sqrt{x^{2}+4}}\right) $$

Prove that if \(x>0, \tan ^{-1} x+\tan ^{-1} \frac{1}{x}=\frac{\pi}{2}\).

In Exercises \(115-116,\) convert each angle to \(D^{\circ} M^{\prime} S^{\prime \prime}\) form. Round your answer to the nearest second. $$ 50.42^{\circ} $$

Use a graphing utility to graph two periodsof the function. Use a graphing utility to graph \(y=\cos x\) and \(y=1-\frac{x^{2}}{2}+\frac{x^{4}}{24}\) in a \(\left[-\pi, \pi, \frac{\pi}{2}\right]\) by \([-2,2,1]\) viewing rectangle. How do the graphs compare?

Use a graphing utility to graph two periods of the function. $$y=0.2 \sin \left(\frac{\pi}{10} x+\pi\right)$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.