In Problems 65-72, find the direction angle of 𝐯. 𝐯=-5 𝐢-5 𝐣...

Key Concepts

Quadrant Considerations

When determining the direction angle using inverse trigonometric functions, it is important to consider the signs of the vector components. The basic arctan function typically returns angles in a restricted range, so adjustments based on the quadrant in which the vector lies are necessary to ensure the angle accurately reflects the vector's orientation in the entire plane.

Inverse Trigonometric Functions

The inverse tangent (arctan) function is commonly used to calculate the initial angle of a vector from its components by taking the ratio of the y-component to the x-component. This function returns an angle whose corresponding tangent value is the given ratio.

Vector Components

In two-dimensional vector analysis, any vector can be described by its components along the horizontal (x-axis) and vertical (y-axis) directions. Understanding how a vector is broken down into these components is foundational, as the direction angle is computed using the ratio of the y-component to the x-component.

Direction Angle

The direction angle of a vector is the angle that the vector makes with the positive x-axis. It is typically measured in degrees (or radians) and represents the orientation of the vector in the plane. Calculating this angle involves using inverse trigonometric functions to determine the appropriate angle based on the vector's components.

In Problems 65-72, find the direction angle of $\mathbf{v}$. $\mathbf{v}=-5 \mathbf{i}-5 \mathbf{j}$

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