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

검증된 단계별 안내

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.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.

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