Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
If a point, P1=[10,10,10], will be rotated by 60 degree about the Z-axis, find the final position P2=[X2,Y2,Z3]
Expert Solution
Step 1
Solution ) suppose P1 [ x1 y1 , z1] is rotated about z axis so new point P2 [ x2 , y2 , z2 ] is given by
x2 = x1cos θ - y1 sin θ
y2 = x1cos θ + y1 sin θ
z2 = z1
[ x1 y1 , z1 ] = [10,10,10]
x2 = 10 cos 60 - 10 sin 60
x2 = 10(1/2) - 10 × (√3/2 )
x2 = 5 - 5√3
y2 = 10 cos60 + 10 sin 60
y2 = 10(1/2) + 10 × (√3/2 )
y2 = 5 + 5 √3
z2 = 10
Hence point will be
P2 = [ 5 - 5 √3 , 5 + 5 √3 , 10 ]
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