/*! 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 24 The point is on the terminal sid... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 24

The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle. $$(-3,-\sqrt{7})$$

Short Answer

Expert verified
The trigonometric values are \(sin = -\sqrt{7}/4\), \(cos = -3/4\), \(tan = \sqrt{7}/3\), \(csc = -4/\sqrt{7}\), \(sec = -4/3\), \(cot = 3/\sqrt{7}\)

Step by step solution

01

Find the Hypotenuse

Determine the radius (hypotenuse) of the triangle formed by the point and the origin. This can be found by applying the Pythagorean theorem, where the hypotenuse \(r\) is given by the equation: \(r = \sqrt{x^2 + y^2}\). Substituting the given coordinates \((-3, -\sqrt{7})\) leads to: \(r = \sqrt{(-3)^2 + (-\sqrt{7})^2} = \sqrt{9 + 7} = \sqrt{16} = 4\)
02

Find Sine, Cosine and Tangent

The sine (sin) is defined as the ratio of 'opposite' (y-coordinate) to hypotenuse (r). The cosine (cos) as the ratio of 'adjacent' (x-coordinate) to hypotenuse (r). The tangent (tan) can be found as the ratio 'opposite' to 'adjacent' (y/x). From the given coordinates and the calculated hypotenuse, the following is found: \(sin = y/r = -\sqrt{7}/4\) , \(cos = x/r = -3/4\) , \(tan = y/x = \sqrt{7}/3\)
03

Find Cosecant, Secant and Cotangent

The cosecant (csc), secant (sec), and cotangent (cot) are the respective reciprocals of sine, cosine, and tangent. Solving for these functions generates the following results: \(csc = r/y = -4/\sqrt{7}\) , \(sec = r/x = -4/3\) , \(cot = x/y = 3/\sqrt{7}\)

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

Your classmate uses a calculator to evaluate \(\tan (\pi / 2)\) and gets a result of 0.0274224385 Describe the error.

Use a graphing utility to graph the logarithmic function. Find the domain, vertical asymptote, and \(x\) -intercept of the logarithmic function. $$f(x)=-\log _{3} x$$

Use a graphing utility to graph the logarithmic function. Find the domain, vertical asymptote, and \(x\) -intercept of the logarithmic function. $$f(x)=\log _{3}(x-4)$$

Define the inverse cosecant function by restricting the domain of the cosecant function to the intervals \([-\pi / 2,0)\) and \((0, \pi / 2],\) and sketch the graph of the inverse function.

True or False Determine whether the statement is true or false. Justify your answer. An example of a bearing used in aviation is \(\mathrm{S} 25^{\circ} \mathrm{W}.\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

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.