/*! 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 2 Find all numbers \(t\) such that... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 2

Find all numbers \(t\) such that \(\left(\frac{3}{5}, t\right)\) is a point on the unit circle.

Short Answer

Expert verified
The possible values of \(t\) that make \(\left(\frac{3}{5},t\right)\) a point on the unit circle are \(t = \frac{4}{5}\) or \(t = -\frac{4}{5}\).

Step by step solution

01

Write down the equation of the unit circle with the given x-coordinate

We know that points on the unit circle satisfy the equation \(x^2 + y^2 = 1\). Replace x with the given x-coordinate, \(\frac{3}{5}\), to get the equation: \[\left(\frac{3}{5}\right)^2 + t^2 = 1\]
02

Solve for the possible values of t

Next, we will solve the equation to find the possible values of the y-coordinate (t). First, square \(\frac{3}{5}\) and simplify: \[\left(\frac{3}{5}\right)^2 = \frac{9}{25}\] Now, we can substitute this value back into the equation and solve for t: \(\frac{9}{25} + t^2 = 1\) To find the possible values of t, first subtract \(\frac{9}{25}\) from both sides of the equation: \(t^2 = 1 - \frac{9}{25}\) Now, simplify the right side of the equation: \(t^2 = \frac{16}{25}\) Lastly, take the square root of both sides: \(t = \pm\frac{4}{5}\)
03

State the solution

Thus, there are two possible values for the y-coordinate (t) that make \(\left(\frac{3}{5},t\right)\) a point on the unit circle: \(t = \frac{4}{5}\) or \(t = -\frac{4}{5}\)

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

Suppose \(u\) and \(v\) are in the interval \(\left(\frac{\pi}{2}, \pi\right),\) with \(\tan u=-2\) and \(\tan v=-3\) Find exact expressions for the indicated quantities. $$ \cos (v-6 \pi) $$

Without using a calculator, sketch the unit circle and the radius that makes an angle of \(\sin ^{-1}(-0.1)\) with the positive horizontal axis.

Explain why $$ |\sin \theta| \leq|\tan \theta| $$ for all \(\theta\) such that \(\tan \theta\) is defined.

Suppose \(u\) and \(v\) are in the interval \(\left(\frac{\pi}{2}, \pi\right),\) with \(\tan u=-2\) and \(\tan v=-3\) Find exact expressions for the indicated quantities. $$ \sin \left(\frac{\pi}{2}-v\right) $$

Show that $$ \cos \left(\tan ^{-1} t\right)=\frac{1}{\sqrt{1+t^{2}}} $$ for every number \(t\).
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

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.