Skip to main content
Ch. 3 - Radian Measure and The Unit Circle
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 3 - Radian Measure and The Unit CircleProblema 58
Capitolo 4, Problema 58

Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)


cos 6

Guida verificata passo dopo passo
1
First, recognize that the angle given is in radians: 6 radians.
Recall that one full rotation (circle) in radians is \(2\pi\), which is approximately \(6.28\) radians.
Since \(6\) radians is slightly less than \(2\pi\) radians, the angle is in the fourth quadrant of the unit circle (between \(\frac{3\pi}{2}\) and \(2\pi\)).
In the fourth quadrant, the cosine function (which corresponds to the x-coordinate on the unit circle) is positive.
Therefore, without calculating the exact value, we conclude that \(\cos 6\) is positive.

Risposta video verificata per un problema simile:

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

Concetti chiave

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

Radian Measure and Quadrantal Angles

Radian measure expresses angles based on the radius of a circle, where 2π radians equal 360°. Quadrantal angles are multiples of π/2 (90°), dividing the circle into four quadrants. Understanding where an angle lies relative to these helps determine the sign of trigonometric functions.
Video consigliato:
Percorso guidato
6:36
Quadratic Formula

Unit Circle and Sign of Trigonometric Functions

The unit circle defines sine and cosine values as coordinates of points on a circle of radius 1. The sign of cosine depends on the x-coordinate, which is positive in the first and fourth quadrants and negative in the second and third. Identifying the quadrant of the angle helps decide the sign of cosine.
Video consigliato:
Percorso guidato
6:34
Sine, Cosine, & Tangent on the Unit Circle

Estimating Angle Position Without a Calculator

To determine the sign of cos(6) without a calculator, approximate 6 radians relative to π (≈3.14). Since 6 is close to 2π (≈6.28), it lies just before completing a full circle, placing it in the fourth quadrant where cosine values are positive.
Video consigliato:
Percorso guidato
05:50
Drawing Angles in Standard Position
Pratica correlata
Domanda del libro di testo

Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).


3.06

927
views
Domanda del libro di testo

Work each problem. See Example 5. Irrigation Area A center-pivot irrigation system provides water to a sector-shaped field as shown in the figure. Find the area of the field if θ = 40.0° and r = 152 yd.

636
views
Domanda del libro di testo

Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).


2

846
views
Domanda del libro di testo

Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)


tan 6.29

697
views
Domanda del libro di testo

Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)


sin 5

699
views
Domanda del libro di testo

Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).


5

792
views