Domanda del libro di testo
Solving equations Solve the following equations.
5(ˣ³) = 29
335
views
Ch. 1 - Functions
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. 1 - Functions210
- Ch. 2 - Limits371
- Ch. 3 - Derivatives633
- Ch. 4 - Applications of the Derivative412
- Ch. 5 - Integration328
- Ch. 6 - Applications of Integration331
- Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions177
- Ch. 8 - Integration Techniques394
- Ch. 9 - Differential Equations179
- Ch. 10 - Sequences and Infinite Series339
- Ch. 11 - Power Series218
- Ch.12 - Parametric and Polar Curves215
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema 1.48
Solving equations Solve each equation.
sin² 2Θ = 1/2, -π/2 ≤ Θ ≤ π/2
Guida verificata passo dopo passo1
Step 1: Recognize that the equation is in the form of \( \sin^2(2\Theta) = \frac{1}{2} \). To solve for \( \Theta \), first take the square root of both sides to get \( \sin(2\Theta) = \pm \frac{1}{\sqrt{2}} \).
Step 2: Recall that \( \sin(2\Theta) = \pm \frac{1}{\sqrt{2}} \) corresponds to angles where the sine function equals \( \frac{1}{\sqrt{2}} \) or \( -\frac{1}{\sqrt{2}} \). These angles are \( \frac{\pi}{4}, \frac{3\pi}{4}, -\frac{\pi}{4}, \) and \( -\frac{3\pi}{4} \).
Step 3: Set \( 2\Theta = \frac{\pi}{4}, \frac{3\pi}{4}, -\frac{\pi}{4}, \) and \( -\frac{3\pi}{4} \) to find the possible values of \( 2\Theta \).
Step 4: Solve for \( \Theta \) by dividing each angle by 2. This gives \( \Theta = \frac{\pi}{8}, \frac{3\pi}{8}, -\frac{\pi}{8}, \) and \( -\frac{3\pi}{8} \).
Step 5: Verify that each solution for \( \Theta \) falls within the given interval \( -\frac{\pi}{2} \leq \Theta \leq \frac{\pi}{2} \).
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:
13mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Trigonometric Functions
Trigonometric functions, such as sine, cosine, and tangent, relate angles to ratios of sides in right triangles. The sine function, specifically, gives the ratio of the length of the opposite side to the hypotenuse. Understanding these functions is crucial for solving equations involving angles, as they provide the foundational relationships needed to manipulate and solve trigonometric equations.
Video consigliato:
Percorso guidato
6:04
Introduction to Trigonometric Functions
Inverse Trigonometric Functions
Inverse trigonometric functions, such as arcsin, arccos, and arctan, are used to find angles when the values of the trigonometric functions are known. For example, if sin(Θ) = 1/2, then Θ can be found using arcsin(1/2). These functions are essential for solving equations where the angle is the unknown, allowing us to determine the angle that corresponds to a given sine, cosine, or tangent value.
Video consigliato:
06:35Derivatives of Other Inverse Trigonometric Functions
Periodic Nature of Trigonometric Functions
Trigonometric functions are periodic, meaning they repeat their values in regular intervals. For sine, the period is 2π, which implies that sin(Θ) = sin(Θ + 2πk) for any integer k. This periodicity is important when solving trigonometric equations, as it allows for multiple solutions within a specified range, such as the interval -π/2 ≤ Θ ≤ π/2 in the given problem.
Video consigliato:
Percorso guidato
6:04Introduction to Trigonometric Functions
Pratica correlata
Domanda del libro di testo
Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.
ƒ(x) = |2x + 1|
351
views
Domanda del libro di testo
Suppose ƒ is an even function with ƒ(2) = 2 and g is an odd function with g(2) = -2. Evaluate ƒ(-2) , ƒ(g(2)), and g(ƒ(-2))
373
views
Domanda del libro di testo
Use the graph of ƒ to find ƒ⁻¹ (2),ƒ⁻¹ (9), and ƒ⁻¹ (12) <IMAGE>
317
views
Domanda del libro di testo
Graph the following functions.
This page contains the following errors:
error on line 1 at column 295: Unescaped '<' not allowed in attributes values
Below is a rendering of the page up to the first error.
363
views
Domanda del libro di testo
Defining piecewise functions Write a definition of the function whose graph is given <IMAGE>
452
views