Domanda del libro di testo
Suppose θ is in the interval (90°, 180°). Find the sign of each of the following. sec(θ + 180°)
604
views
Ch. 2 - Acute Angles and Right Triangles
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 3, Problema 85
Concept Check Work each problem. Without using a calculator, determine which of the following numbers is closest to sin 115°: -0.9, -0.1, 0, 0.1, or 0.9.
Guida verificata passo dopo passo1
Recall that the sine function is positive in the second quadrant, where angles range from 90° to 180°. Since 115° is in the second quadrant, \(\sin 115^\circ\) is positive.
Use the reference angle to find the sine value. The reference angle for 115° is \(180^\circ - 115^\circ = 65^\circ\). So, \(\sin 115^\circ = \sin 65^\circ\).
Remember that \(\sin 65^\circ\) is a positive value less than 1 but closer to 1 than to 0, because 65° is closer to 90° than to 0°.
Compare the given options (-0.9, -0.1, 0, 0.1, 0.9) with the expected value of \(\sin 65^\circ\). Since \(\sin 65^\circ\) is positive and relatively large, the closest number should be positive and near 0.9.
Conclude that among the given options, 0.9 is the closest to \(\sin 115^\circ\) based on the properties of the sine function and the reference angle.
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:
3mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Unit Circle and Angle Measurement
The unit circle represents angles and their corresponding sine values on a circle of radius one. Angles are measured in degrees or radians, and sine corresponds to the y-coordinate of the point on the circle. Understanding where 115° lies helps estimate the sine value without a calculator.
Video consigliato:
Percorso guidato
06:11
Introduction to the Unit Circle
Sine Function Properties in Different Quadrants
Sine values vary depending on the quadrant of the angle. Since 115° is in the second quadrant (90° to 180°), sine values are positive and decrease from 1 at 90° to 0 at 180°. This knowledge helps narrow down the possible sine values for 115°.
Video consigliato:
Percorso guidato
6:12Solving Quadratic Equations by the Square Root Property
Reference Angles and Approximation
A reference angle is the acute angle formed with the x-axis, used to find sine values of angles in other quadrants. For 115°, the reference angle is 65°. Knowing sine 65° is about 0.91 helps approximate sine 115° as positive and close to 0.9.
Video consigliato:
Percorso guidato
5:31Reference Angles on the Unit Circle
Pratica correlata
Domanda del libro di testo
Concept Check Work each problem. For what angles θ between 0° and 360° is cos θ = sin θ true?
667
views
Domanda del libro di testo
Suppose θ is in the interval (90°, 180°). Find the sign of each of the following. cot(θ + 180°)
544
views
Domanda del libro di testo
Suppose θ is in the interval (90°, 180°). Find the sign of each of the following. sin(-θ)
426
views