In Problems 59-64, write the vector 𝐯 in the form a +b 𝐣, given its magnitude 𝐯 and the angle αi

Name: Problem 63, Chapter 8: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2021-07-01T17:19:41-08:00
Duration: 1 min 45 s
Channel: Allison Knapp
Description: In Problems 59-64, write the vector 𝐯 in the form a +b 𝐣, given its magnitude 𝐯 and the angle αit makes with the positive x-axis. 𝐯=25, α=330^∘

step 1 So for this problem, we are trying to rate the standard form in I and J of the vector with a mag

Question

In Problems 59-64, write the vector $\mathbf{v}$ in the form a $+b \mathbf{j}$, given its magnitude $\|\mathbf{v}\|$ and the angle $\alpha$ it makes with the positive $x$-axis. $\|\mathbf{v}\|=25, \quad \alpha=330^{\circ}$

   In Problems 59-64, write the vector $\mathbf{v}$ in the form a $+b \mathbf{j}$, given its magnitude $\|\mathbf{v}\|$ and the angle $\alpha$ it makes with the positive $x$-axis.
 $\|\mathbf{v}\|=25, \quad \alpha=330^{\circ}$

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

Michael Sullivan 4th Edition

Chapter 8, Problem 63

Instant Answer

Solved by Expert Allison Knapp

07/01/2021

Step 1

We can use the formula $\text{radians} = \frac{\pi}{180} \times \text{degrees}$. So, $\alpha = 330^\circ \times \frac{\pi}{180} = \frac{11\pi}{6}$ radians. Show more…

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In Problems 59-64, write the vector $\mathbf{v}$ in the form a $+b \mathbf{j}$, given its magnitude $\|\mathbf{v}\|$ and the angle $\alpha$ it makes with the positive $x$-axis. $\|\mathbf{v}\|=25, \quad \alpha=330^{\circ}$

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Key Concepts

Vector Representation in Component Form

This concept involves expressing a vector as a combination of its horizontal and vertical components using standard unit vectors. This method simplifies vector analysis by breaking down the vector into parts that align with the coordinate axes.

Trigonometric Decomposition of Vectors

This process uses trigonometric functions—specifically cosine and sine—to determine the components of a vector based on its magnitude and the angle it makes with the positive x-axis. The cosine function is used for the horizontal component, while the sine function is used for the vertical component.

Angle Measurement in Standard Position

Angles measured from the positive x-axis are described in standard position, which is crucial for determining the correct signs and magnitudes of the vector components. Understanding standard position helps in addressing problems where the vector is oriented in various quadrants.

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