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Popular Trigonometry >

sin(2x)=1.47(sin(x))^2

  • Pre Algebra
  • Algebra
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Solution

sin(2x)=1.47(sin(x))2

Solution

x=2πn,x=π+2πn,x=0.93696…+πn
+1
Degrees
x=0∘+360∘n,x=180∘+360∘n,x=53.68411…∘+180∘n
Solution steps
sin(2x)=1.47(sin(x))2
Subtract 1.47(sin(x))2 from both sidessin(2x)−1.47sin2(x)=0
Rewrite using trig identities
sin(2x)−1.47sin2(x)
Use the Double Angle identity: sin(2x)=2sin(x)cos(x)=2sin(x)cos(x)−1.47sin2(x)
−1.47sin2(x)+2cos(x)sin(x)=0
Factor −1.47sin2(x)+2cos(x)sin(x):sin(x)(−1.47sin(x)+2cos(x))
−1.47sin2(x)+2cos(x)sin(x)
Apply exponent rule: ab+c=abacsin2(x)=sin(x)sin(x)=−1.47sin(x)sin(x)+2sin(x)cos(x)
Factor out common term sin(x)=sin(x)(−1.47sin(x)+2cos(x))
sin(x)(−1.47sin(x)+2cos(x))=0
Solving each part separatelysin(x)=0or−1.47sin(x)+2cos(x)=0
sin(x)=0:x=2πn,x=π+2πn
sin(x)=0
General solutions for sin(x)=0
sin(x) periodicity table with 2πn cycle:
x06π​4π​3π​2π​32π​43π​65π​​sin(x)021​22​​23​​123​​22​​21​​xπ67π​45π​34π​23π​35π​47π​611π​​sin(x)0−21​−22​​−23​​−1−23​​−22​​−21​​​
x=0+2πn,x=π+2πn
x=0+2πn,x=π+2πn
Solve x=0+2πn:x=2πn
x=0+2πn
0+2πn=2πnx=2πn
x=2πn,x=π+2πn
−1.47sin(x)+2cos(x)=0:x=arctan(147200​)+πn
−1.47sin(x)+2cos(x)=0
Rewrite using trig identities
−1.47sin(x)+2cos(x)=0
Divide both sides by cos(x),cos(x)=0cos(x)−1.47sin(x)+2cos(x)​=cos(x)0​
Simplify−cos(x)1.47sin(x)​+2=0
Use the basic trigonometric identity: cos(x)sin(x)​=tan(x)−1.47tan(x)+2=0
−1.47tan(x)+2=0
Multiply both sides by 100
−1.47tan(x)+2=0
To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are 2digits to the right of the decimal point, therefore multiply by 100−1.47tan(x)⋅100+2⋅100=0⋅100
Refine−147tan(x)+200=0
−147tan(x)+200=0
Move 200to the right side
−147tan(x)+200=0
Subtract 200 from both sides−147tan(x)+200−200=0−200
Simplify−147tan(x)=−200
−147tan(x)=−200
Divide both sides by −147
−147tan(x)=−200
Divide both sides by −147−147−147tan(x)​=−147−200​
Simplifytan(x)=147200​
tan(x)=147200​
Apply trig inverse properties
tan(x)=147200​
General solutions for tan(x)=147200​tan(x)=a⇒x=arctan(a)+πnx=arctan(147200​)+πn
x=arctan(147200​)+πn
Combine all the solutionsx=2πn,x=π+2πn,x=arctan(147200​)+πn
Show solutions in decimal formx=2πn,x=π+2πn,x=0.93696…+πn

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2sin^2(u)=1+,u8.5=12sin(a)cos(x)= 1/15cot(θ)=-sqrt(3),0<= θ<2pi(sin(90))/(458.912)=(sin(x))/(450)

Frequently Asked Questions (FAQ)

  • What is the general solution for sin(2x)=1.47(sin(x))^2 ?

    The general solution for sin(2x)=1.47(sin(x))^2 is x=2pin,x=pi+2pin,x=0.93696…+pin
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