Question

In Problems 65-72, find the direction angle of $\mathbf{v}$. $\mathbf{v}=3 \mathbf{i}+3 \mathbf{j}$

   In Problems 65-72, find the direction angle of $\mathbf{v}$.
 $\mathbf{v}=3 \mathbf{i}+3 \mathbf{j}$

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan 4th Edition

Chapter 8, Problem 65

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In this case, $\mathbf{v} = 3\mathbf{i} + 3\mathbf{j}$. This means the vector $\mathbf{v}$ has an x-component of 3 and a y-component of 3. Show more…

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In Problems 65-72, find the direction angle of $\mathbf{v}$. $\mathbf{v}=3 \mathbf{i}+3 \mathbf{j}$

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Key Concepts

Inverse Tangent Function

The arctan function is used to compute the angle whose tangent equals the ratio of the y-component to the x-component. This function is crucial for translating from a vector's component form to its angular direction.

Direction Angle

The direction angle of a vector is the angle it makes with the positive x-axis. It is determined by relating the vector's components through trigonometric ratios, typically using the inverse tangent function to convert the ratio of the y-component to the x-component into an angle.

Vector Components

Vectors in the plane are expressed in terms of components along the standard basis vectors (i and j). This representation enables calculation of properties like magnitude and direction by breaking the vector into its horizontal and vertical parts.

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