Let θ be the angle that the vector A makes with the +x-axis, measured counterclockwise from that axis. Find angle θ for a vector that has these components: A_x = 2.00m, A_y = −1.00 m

검증된 단계별 안내

Start by understanding that the angle θ is the angle between the vector A and the positive x-axis. This angle can be found using trigonometric functions, specifically the tangent function, which relates the opposite side to the adjacent side in a right triangle.

The components of the vector A are given as Ax = 2.00 m and Ay = -1.00 m. These components represent the horizontal and vertical sides of the triangle formed by the vector.

Use the tangent function to find the angle θ. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Therefore, tan(θ) = Ay / Ax. Substitute the given values into this equation: tan(θ) = -1.00 m / 2.00 m.

To find the angle θ, take the arctangent (inverse tangent) of the ratio calculated in the previous step. This will give you θ = arctan(-1.00 m / 2.00 m).

Since the tangent function can have multiple solutions, consider the direction of the vector components. The negative Ay indicates that the vector is pointing downward, so the angle θ will be in the fourth quadrant. Adjust the angle accordingly to ensure it is measured counterclockwise from the positive x-axis.

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.

Vector Components

Vector components are the projections of a vector along the axes of a coordinate system. In this problem, Ax and Ay represent the horizontal and vertical components of vector A, respectively. Understanding these components is crucial for determining the direction and magnitude of the vector.

Trigonometric Functions

Trigonometric functions, such as tangent, sine, and cosine, relate the angles and sides of a right triangle. To find the angle θ that a vector makes with the x-axis, the tangent function is used, defined as the ratio of the opposite side (Ay) to the adjacent side (Ax). This relationship helps calculate the angle from the vector components.

Inverse Trigonometric Functions

Inverse trigonometric functions, like arctan, are used to find angles from known ratios of sides. In this context, arctan(Ay/Ax) will yield the angle θ that the vector makes with the +x-axis. This function is essential for converting the component ratio into an angle measurement.