Solutions
Integral CalculatorDerivative CalculatorAlgebra CalculatorMatrix CalculatorMore...
Graphing
Line Graph CalculatorExponential Graph CalculatorQuadratic Graph CalculatorSin graph CalculatorMore...
Calculators
BMI CalculatorCompound Interest CalculatorPercentage CalculatorAcceleration CalculatorMore...
Geometry
Pythagorean Theorem CalculatorCircle Area CalculatorIsosceles Triangle CalculatorTriangles CalculatorMore...
Tools
NotebookGroupsCheat SheetsWorksheetsPracticeVerify
en
English
Español
Português
Français
Deutsch
Italiano
Русский
中文(简体)
한국어
日本語
Tiếng Việt
עברית
العربية
Popular Trigonometry >

sin(4x)=cos(x/2)

  • Pre Algebra
  • Algebra
  • Pre Calculus
  • Calculus
  • Functions
  • Linear Algebra
  • Trigonometry
  • Statistics
  • Physics
  • Chemistry
  • Finance
  • Economics
  • Conversions

Solution

sin(4x)=cos(2x​)

Solution

NoSolutionforx∈R
Solution steps
sin(4x)=cos(2x​)
Rewrite using trig identities
sin(4x)=cos(2x​)
Use the following identity: cos(x)=sin(2π​−x)sin(4x)=sin(2π​−2x​)
sin(4x)=sin(2π​−2x​)
Apply trig inverse properties
sin(4x)=sin(2π​−2x​)
sin(x)=sin(y)⇒x=y+2πn,x=π−y+2πn4x=2π​−2x​+2πn,4x=π−(2π​−2x​)+2πn
4x=2π​−2x​+2πn,4x=π−(2π​−2x​)+2πn
4x=2π​−2x​+2πn:x=9π+4πn​
4x=2π​−2x​+2πn
Move 2x​to the left side
4x=2π​−2x​+2πn
Add 2x​ to both sides4x+2x​=2π​−2x​+2πn+2x​
Simplify
4x+2x​=2π​−2x​+2πn+2x​
Simplify 4x+2x​:29x​
4x+2x​
Convert element to fraction: 4x=24x2​=2x​+24x⋅2​
Since the denominators are equal, combine the fractions: ca​±cb​=ca±b​=2x+4x⋅2​
x+4x⋅2=9x
x+4x⋅2
Multiply the numbers: 4⋅2=8=x+8x
Add similar elements: x+8x=9x=9x
=29x​
Simplify 2π​−2x​+2πn+2x​:2π​+2πn
2π​−2x​+2πn+2x​
Add similar elements: −2x​+2x​=0
=2π​+2πn
29x​=2π​+2πn
29x​=2π​+2πn
29x​=2π​+2πn
Multiply both sides by 2
29x​=2π​+2πn
Multiply both sides by 222⋅9x​=2⋅2π​+2⋅2πn
Simplify
22⋅9x​=2⋅2π​+2⋅2πn
Simplify 22⋅9x​:9x
22⋅9x​
Multiply the numbers: 2⋅9=18=218x​
Divide the numbers: 218​=9=9x
Simplify 2⋅2π​+2⋅2πn:π+4πn
2⋅2π​+2⋅2πn
2⋅2π​=π
2⋅2π​
Multiply fractions: a⋅cb​=ca⋅b​=2π2​
Cancel the common factor: 2=π
2⋅2πn=4πn
2⋅2πn
Multiply the numbers: 2⋅2=4=4πn
=π+4πn
9x=π+4πn
9x=π+4πn
9x=π+4πn
Divide both sides by 9
9x=π+4πn
Divide both sides by 999x​=9π​+94πn​
Simplify
99x​=9π​+94πn​
Simplify 99x​:x
99x​
Divide the numbers: 99​=1=x
Simplify 9π​+94πn​:9π+4πn​
9π​+94πn​
Apply rule ca​±cb​=ca±b​=9π+4πn​
x=9π+4πn​
x=9π+4πn​
x=9π+4πn​
4x=π−(2π​−2x​)+2πn:x=7π+4πn​
4x=π−(2π​−2x​)+2πn
Move (2π​−2x​)to the left side
4x=π−(2π​−2x​)+2πn
Add (2π​−2x​) to both sides4x+2π​−2x​=π−(2π​−2x​)+2πn+2π​−2x​
Simplify
4x+2π​−2x​=π−(2π​−2x​)+2πn+2π​−2x​
Simplify 4x+2π​−2x​:2π+7x​
4x+2π​−2x​
Combine the fractions 2π​−2x​:2π−x​
Apply rule ca​±cb​=ca±b​=2π−x​
=4x+2−x+π​
Convert element to fraction: 4x=24x2​=2π−x​+24x⋅2​
Since the denominators are equal, combine the fractions: ca​±cb​=ca±b​=2π−x+4x⋅2​
π−x+4x⋅2=π+7x
π−x+4x⋅2
Multiply the numbers: 4⋅2=8=π−x+8x
Add similar elements: −x+8x=7x=π+7x
=2π+7x​
Simplify π−(2π​−2x​)+2πn+2π​−2x​:π+2πn
π−(2π​−2x​)+2πn+2π​−2x​
Add similar elements: −(2π​−2x​)+2π​−2x​=0
=π+2πn
2π+7x​=π+2πn
2π+7x​=π+2πn
2π+7x​=π+2πn
Multiply both sides by 2
2π+7x​=π+2πn
Multiply both sides by 222(π+7x)​=2π+2⋅2πn
Simplifyπ+7x=2π+4πn
π+7x=2π+4πn
Move πto the right side
π+7x=2π+4πn
Subtract π from both sidesπ+7x−π=2π+4πn−π
Simplify7x=π+4πn
7x=π+4πn
Divide both sides by 7
7x=π+4πn
Divide both sides by 777x​=7π​+74πn​
Simplify
77x​=7π​+74πn​
Simplify 77x​:x
77x​
Divide the numbers: 77​=1=x
Simplify 7π​+74πn​:7π+4πn​
7π​+74πn​
Apply rule ca​±cb​=ca±b​=7π+4πn​
x=7π+4πn​
x=7π+4πn​
x=7π+4πn​
Since the equation is undefined for:9π+4πn​,7π+4πn​NoSolutionforx∈R

Graph

Sorry, your browser does not support this application
View interactive graph

Popular Examples

solvefor a,cos(a-b)=2cos(pi/2-x)tan(x)-sec(-x)=1(cot(θ)+csc(θ))/(sec(θ)+1)=sin(θ)1/(cos(2x))+tan(2x)=3cos(2x),0<x<90sin(x)= 4/5 ,0<= x<2pi

Frequently Asked Questions (FAQ)

  • What is the general solution for sin(4x)=cos(x/2) ?

    The general solution for sin(4x)=cos(x/2) is No Solution for x\in\mathbb{R}
Study ToolsAI Math SolverPopular ProblemsWorksheetsStudy GuidesPracticeCheat SheetsCalculatorsGraphing CalculatorGeometry CalculatorVerify Solution
AppsSymbolab App (Android)Graphing Calculator (Android)Practice (Android)Symbolab App (iOS)Graphing Calculator (iOS)Practice (iOS)Chrome ExtensionSymbolab Math Solver API
CompanyAbout SymbolabBlogHelp
LegalPrivacyTermsCookie PolicyCookie SettingsDo Not Sell or Share My Personal InfoCopyright, Community Guidelines, DSA & other Legal ResourcesLearneo Legal Center
Social Media
Symbolab, a Learneo, Inc. business
© Learneo, Inc. 2024