/*! 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 34 Write the expression as the sine... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 34

Write the expression as the sine, cosine, or tangent of an angle. $$\frac{\tan 140^{\circ}-\tan 60^{\circ}}{1+\tan 140^{\circ} \tan 60^{\circ}}$$

Short Answer

Expert verified
The given expression simplifies to \( \tan 80^{\circ} \).

Step by step solution

01

Identify the formula

Recognize the given expression matches the formula for the tangent of the difference of two angles: \( \tan (A-B) = \frac{\tan A-\tan B}{1+\tan A \tan B} \). Here, 140 degrees is A and 60 degrees is B.
02

Apply the formula

Replace A with 140 degrees and B with 60 degrees in the tangent difference formula. This renders \( \tan (140^{\circ}-60^{\circ}) \) as the expression in the given format.
03

Simplify the result

Perform the operation in the parentheses - subtract 60 degrees from 140 degrees, which equals 80 degrees. Thus, the expression \( \tan (140^{\circ}-60^{\circ}) \) simplifies to \( \tan 80^{\circ} \).

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

Find the exact values of the sine, cosine, and tangent of the angle. $$\frac{17 \pi}{12}=\frac{9 \pi}{4}-\frac{5 \pi}{6}$$

Find the exact values of the sine, cosine, and tangent of the angle. $$\frac{13 \pi}{12}$$

Find the exact values of the sine, cosine, and tangent of the angle. $$285^{\circ}$$

Find the exact values of the sine, cosine, and tangent of the angle. $$-\frac{13 \pi}{12}$$

Fill in the blank. \(\sin (u+v)=\)_____
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

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.