Domanda del libro di testo
The graph of a cotangent function is given. Select the equation for each graph from the following options: y = cot(x + π/2), y = cot(x + π), y = −cot x, y= −cot(x − π/2).
1996
views
Ch. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
Tutti i libri di testo
Blitzer 3rd EditionCh. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric FunctionsProblema 13
Blitzer 3rd EditionCh. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric FunctionsProblema 13Capitolo 2, Problema 13
In Exercises 1–26, find the exact value of each expression. _ tan⁻¹ √3/3
Guida verificata passo dopo passo1
Recognize that the expression \( \tan^{-1} \left( \frac{\sqrt{3}}{3} \right) \) represents the angle whose tangent is \( \frac{\sqrt{3}}{3} \).
Recall the common tangent values for special angles: \( \tan 30^\circ = \tan \frac{\pi}{6} = \frac{\sqrt{3}}{3} \).
Since the inverse tangent function \( \tan^{-1} \) returns the angle in the range \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \), identify the angle corresponding to \( \frac{\sqrt{3}}{3} \) within this interval.
Conclude that \( \tan^{-1} \left( \frac{\sqrt{3}}{3} \right) = \frac{\pi}{6} \) radians (or 30 degrees).
Express the exact value in radians or degrees as required by the problem.
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:
2mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Inverse Tangent Function (tan⁻¹ or arctan)
The inverse tangent function, denoted as tan⁻¹ or arctan, returns the angle whose tangent is a given number. It is used to find an angle when the ratio of the opposite side to the adjacent side in a right triangle is known.
Video consigliato:
Percorso guidato
3:17
Inverse Tangent
Exact Values of Special Angles
Certain angles have well-known exact trigonometric values, such as tan(30°) = √3/3. Recognizing these special angles allows for finding exact values without a calculator, which is essential for solving inverse trigonometric expressions.
Video consigliato:
Percorso guidato
04:3945-45-90 Triangles
Relationship Between Tangent and Angles in Right Triangles
Tangent of an angle in a right triangle is the ratio of the length of the opposite side to the adjacent side. Understanding this ratio helps interpret the inverse tangent function and connect numeric values to specific angles.
Video consigliato:
Percorso guidato
5:19Solving Right Triangles with the Pythagorean Theorem
Pratica correlata
Domanda del libro di testo
Determine the amplitude and period of each function. Then graph one period of the function. y = -3 sin 2πx
1173
views
Domanda del libro di testo
In Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = sin(x − π)
1028
views
Domanda del libro di testo
In Exercises 12–13, use a vertical shift to graph one period of the function. y = 2 cos 1/3 x − 2
962
views
Domanda del libro di testo
In Exercises 7–16, determine the amplitude and period of each function. Then graph one period of the function. y = -sin 2/3 x
895
views
Domanda del libro di testo
In Exercises 14–15, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = sin x + cos 1/2 x
791
views