Skip to main content
Ch. 1 - Angles and the Trigonometric Functions
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 3rd EditionCh. 1 - Angles and the Trigonometric FunctionsProblema 1.1.64
Capitolo 1, Problema 1.1.64

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. 17𝜋 /5

Guida verificata passo dopo passo
1
Understand that two angles are coterminal if they differ by an integer multiple of \(2\pi\). This means we can add or subtract \(2\pi\) to the given angle to find coterminal angles.
Given the angle \(\frac{17\pi}{5}\), we want to find a positive angle \(\theta\) such that \(0 \leq \theta < 2\pi\) and \(\theta\) is coterminal with \(\frac{17\pi}{5}\).
To do this, subtract multiples of \(2\pi\) from \(\frac{17\pi}{5}\) until the result lies between \(0\) and \(2\pi\). Express \(2\pi\) with denominator 5 as \(\frac{10\pi}{5}\) for easier subtraction.
Calculate \(\frac{17\pi}{5} - 2\pi = \frac{17\pi}{5} - \frac{10\pi}{5} = \frac{7\pi}{5}\). Since \(\frac{7\pi}{5}\) is positive and less than \(2\pi\), this is the coterminal angle you are looking for.
Verify that \(0 \leq \frac{7\pi}{5} < 2\pi\) to confirm the angle is within the desired range.

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:
2m

Concetti chiave

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

Coterminal Angles

Coterminal angles are angles that share the same initial and terminal sides but differ by full rotations of 2π radians. To find a coterminal angle, you add or subtract multiples of 2π until the angle lies within the desired range, such as between 0 and 2π.
Video consigliato:
Percorso guidato
04:46
Coterminal Angles

Angle Measurement in Radians

Angles can be measured in radians, where 2π radians equal one full rotation (360 degrees). Understanding how to convert and manipulate angles in radians is essential for solving problems involving coterminal angles and angle normalization.
Video consigliato:
Percorso guidato
5:04
Converting between Degrees & Radians

Finding Positive Angles Less Than or Equal to 2π

To find a positive angle less than or equal to 2π that is coterminal with a given angle, subtract multiples of 2π from the angle until the result is within the interval [0, 2π]. This process ensures the angle is expressed in its principal value range.
Video consigliato:
Percorso guidato
05:50
Drawing Angles in Standard Position
Pratica correlata
Domanda del libro di testo

In Exercises 35–60, find the reference angle for each angle. -13𝜋/3

629
views
Domanda del libro di testo

In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator. tan(-𝜋/4)

753
views
Domanda del libro di testo

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

-210°

649
views
Domanda del libro di testo

In Exercises 59–62, use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places. tan θ = 0.4169

670
views
Domanda del libro di testo

In Exercises 63–68, find the exact value of each expression. Do not use a calculator. 1 + sin² 40° + sin² 50°

601
views
Domanda del libro di testo

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. -𝜋/40

659
views