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()

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