University:
York University
Course:
MATH 1013 | Applied Calculus
Academic year:

2023
Views:

422

Pages:

1
Author:

Niklas

IV. Trigonometric Equations MULTIPLE ANGLE EQUATIONS AND QUADRATIC EQUATIONS (Ch.5) I. MULTIPLE ANGLE EQUATIONS: ↳ for ax=f^-1(k) find solutions on [0°,(360a)°] or [0,2πa) to f^-1(k). solve 2sin2x=√3 for x∈[0,2π) sin2x=√3/2 2x∈{π/3,2π/3,7π/3,8π/3} 2 ROTATIONS {π/6,π/3,7π/6,4π/3} solve 5cos(x/2)+7=3 for x∈[0°,360°) 5cos(x/2)=-4 cos(x/2)=-4/5 x/2∈{143°,317°}=(2·217)°∉[0°,360°) {286°} solve 7tan3x-2√3tan3x for x∈[0,2π) 6tan3x=2√3 tan3x=√3/3 3x∈{π/6,π/2,7π/6,11π/6,17π/6,19π/6} {π/18,π/6,7π/18,11π/18,17π/18,19π/18} II. QUADRATIC EQUATIONS solve cos²x-7/2cosx-2=0 for x∈[0,2π) solve tanxcos²x-tanx for tanx(cos²x-1)=0 tanx=0 (cos²x=1 {0°,180°} cosx=1 cosx=-1 {0°,180°} 2cos²x-7cosx-4=0 t05χ=(7±√(49-4(-9)))/4 cosx=(7±9)/4 cosx=4 x∉ℝ cosx=-1/2 {2π/3,4π/3} {2π/3,4π/3}