Ch. 2 - Acute Angles and Right Triangles

Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo

Lial 12th Edition

Ch. 2 - Acute Angles and Right Triangles

Problema 19

Capitolo 3, Problema 19

Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. 300°

Guida verificata passo dopo passo

Recognize that the angle 300° is in the fourth quadrant of the unit circle, where cosine is positive and sine is negative.

Find the reference angle by subtracting 300° from 360°, which gives \(360° - 300° = 60°\).

Recall the exact values of sine and cosine for the reference angle 60°: \(\sin 60° = \frac{\sqrt{3}}{2}\) and \(\cos 60° = \frac{1}{2}\).

Determine the sine and cosine of 300° using the signs in the fourth quadrant: \(\sin 300° = -\sin 60° = -\frac{\sqrt{3}}{2}\) and \(\cos 300° = \cos 60° = \frac{1}{2}\).

Calculate the remaining four trigonometric functions using the definitions: \(\tan 300° = \frac{\sin 300°}{\cos 300°}\), \(\csc 300° = \frac{1}{\sin 300°}\), \(\sec 300° = \frac{1}{\cos 300°}\), and \(\cot 300° = \frac{1}{\tan 300°}\). Remember to rationalize denominators where necessary.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Unit Circle and Angle Measurement

The unit circle is a circle with radius 1 centered at the origin, used to define trigonometric functions for all angles. Angles like 300° correspond to specific points on the unit circle, where coordinates (x, y) represent cosine and sine values respectively. Understanding how to locate angles on the unit circle is essential for finding exact trigonometric values.

Video consigliato:

Percorso guidato

06:11

Introduction to the Unit Circle

Definition of the Six Trigonometric Functions

The six trigonometric functions are sine, cosine, tangent, cosecant, secant, and cotangent. Sine and cosine are based on the y and x coordinates of the unit circle point, while tangent is sine divided by cosine. The reciprocal functions (cosecant, secant, cotangent) are the inverses of sine, cosine, and tangent respectively, and knowing these definitions helps compute all values.

Video consigliato:

Percorso guidato

6:04

Introduction to Trigonometric Functions

Rationalizing Denominators

Rationalizing denominators involves eliminating radicals from the denominator of a fraction by multiplying numerator and denominator by a suitable expression. This process is important for expressing exact trigonometric values in a simplified and standardized form, especially when the denominator contains square roots, ensuring clarity and consistency in answers.

Video consigliato:

Percorso guidato

2:58

Rationalizing Denominators

Pratica correlata

Domanda del libro di testo

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. cos θ = -½

667

views

Domanda del libro di testo

Solve each right triangle. When two sides are given, give angles in degrees and minutes.

512

views

Domanda del libro di testo

Evaluate each expression. Give exact values. tan² 120° - 2 cot 240°

570

views

Domanda del libro di testo

Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. 405°

721

views

Domanda del libro di testo

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. sec θ = -2√3 3

630

views

Domanda del libro di testo

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Use the Pythagorean theorem to find the unknown side length. Then find exact values of the six trigonometric functions for angle B. Rationalize denominators when applicable. See Example 1. a = √2, c = 2

860

views