   Chapter 12.5, Problem 4E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# 3-8 ■ Rotation of Axes Determine the XY-coordinates of the given point if the coordinate axes are rotated through the indicated angle ( − 2 , 1 ) , ϕ = 30 ∘

To determine

The XY-coordinates of the given point (2,1) and the coordinate axes are rotated through at ϕ=30.

Explanation

Given:

The XY-coordinates of the given point is (2,1) and the coordinate axes are rotated through at angle ϕ=30.

Approach:

The x-axes and y-axes in a coordinate plane are rotated through the acute angle ϕ to produce the X-axis and Y-axis. Then, the coordinates (x,y) and (X,Y) of a point in the xy and the XY-planes are

X=xcosϕ+ysinϕ …… (1)

Y=xsinϕ+ycosϕ …… (2)

Here, (x,y) is the coordinates of the point and ϕ is the angle at which coordinate axis are rotated.

Calculation:

Substitute 2 for x, 1 for y and 30 for ϕ in equation (1).

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 