Solve each equation for x.
4/3 arctan x/2 = π

Guida verificata passo dopo passo

Start by isolating the arctan expression. Multiply both sides of the equation by \( \frac{3}{4} \) to get \( \arctan \left( \frac{x}{2} \right) = \frac{3}{4} \pi \).

Recall that \( \arctan(y) = \theta \) means \( \tan(\theta) = y \). So rewrite the equation as \( \tan \left( \frac{3}{4} \pi \right) = \frac{x}{2} \).

Evaluate \( \tan \left( \frac{3}{4} \pi \right) \) by considering the unit circle or known tangent values at special angles.

Once you find \( \tan \left( \frac{3}{4} \pi \right) \), set it equal to \( \frac{x}{2} \) and solve for \( x \) by multiplying both sides by 2.

Remember to consider the domain and range of the arctan function and check if there are any additional solutions based on the periodicity of the tangent function.

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.

Inverse Trigonometric Functions (Arctan)

The arctan function is the inverse of the tangent function, returning the angle whose tangent is a given number. It is essential for solving equations where the variable is inside a tangent function, allowing us to isolate the variable by applying arctan to both sides.

Video consigliato:

Percorso guidato

4:28

Introduction to Inverse Trig Functions

Solving Equations Involving Fractions and π

Equations involving fractions and π require careful manipulation of constants and variables. Understanding how to isolate the variable by multiplying or dividing both sides, and recognizing the value of π (approximately 3.1416), is crucial for accurate solutions.

Video consigliato:

Percorso guidato

4:02

Solving Linear Equations with Fractions

Algebraic Manipulation and Isolation of Variables

Algebraic skills are necessary to isolate the variable x after applying inverse functions. This includes multiplying both sides by constants, simplifying expressions, and solving for x step-by-step to find the exact or approximate solution.

Video consigliato:

Percorso guidato