Compute the result of counterclockwise rotation of a vector =sin (a)fƏx8α Ω[3] ₁Eby an angle = 1π.

Answered: Compute the result of counterclockwise…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Compute the result of counterclockwise rotation of a vector =
sin (a)
f
Əx
8
α Ω
[3] ₁
E
by an angle = 1
π.

Expert Solution

Step 1: Given data

If a vector $v$ is rotated counterclockwise about the origin through an angle $θ$ then the resultant vector $v_{1}$ is given by,

$v_{1} = (\begin{matrix} \cos (θ) & - \sin (θ) \\ \sin (θ) & \cos (θ) \end{matrix}) v$

Where the matrix

(\begin{matrix} \cos (θ) & - \sin (θ) \\ \sin (θ) & \cos (θ) \end{matrix})

is the rotation matrix.

The given vector is

v = (\begin{matrix} 2 \\ 3 \end{matrix})

The given angle is

θ = \frac{3 π}{4}

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Compute the result of counterclockwise rotation of a vector a = absin (a) 81 ∞as 23 by an angle = ³.