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Get Full Access to Linear Algebra With Applications - 8 Edition - Chapter 5.4 - Problem 8
Get Full Access to Linear Algebra With Applications - 8 Edition - Chapter 5.4 - Problem 8

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# Let a rectangular xy-coordinate system be given and a second rectangular coordinate ISBN: 9781449679545 435

## Solution for problem 8 Chapter 5.4

Linear Algebra with Applications | 8th Edition

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Problem 8

Let a rectangular xy-coordinate system be given and a second rectangular coordinate system x'y' be obtained from it through a rotation through an angle () about the origin. An arbitrary point Pin the plane has coordinates [] relative to the xy-coordinate system and coordinates [:] relative to the x'y'-coordinate system. Use trigonometry to prove that the coordinate transformation is x' = x cos() + y sin() y' = x sin() + y cos()

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MATH121 CHHA APPTTEER R4NOOT TEESS Lesson4.5–CombiningFunctions EXAMPLE1. Find(f°g)(2),whenf(x)=x +1andg(x)=x +x . 3 2 (First,weneedtofindthefunctiong(2).) g(2)=2 +2 =12 (Now,substitutethevalue12inforxinthe functionf(x).) f(12)=12 +1=145 (f°g)(2)=145

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##### ISBN: 9781449679545

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