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(135-x)=sin(x)

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

Solution

sin(135−x)=sin(x)

Solution

x=−2πn+2135​,x=−π+2135​−2πn
+1
Degrees
x=3867.46511…∘−360∘n,x=3687.46511…∘−360∘n
Solution steps
sin(135−x)=sin(x)
Subtract sin(x) from both sidessin(135−x)−sin(x)=0
Rewrite using trig identities
sin(135−x)−sin(x)
Use the Sum to Product identity: sin(s)−sin(t)=2sin(2s−t​)cos(2s+t​)=2sin(2135−x−x​)cos(2135−x+x​)
Simplify 2sin(2135−x−x​)cos(2135−x+x​):2cos(2135​)sin(2135−2x​)
2sin(2135−x−x​)cos(2135−x+x​)
Add similar elements: −x−x=−2x=2sin(2−2x+135​)cos(2x−x+135​)
Add similar elements: −x+x=0=2cos(2135​)sin(2−2x+135​)
=2cos(2135​)sin(2135−2x​)
2cos(2135​)sin(2135−2x​)=0
Divide both sides by 2cos(2135​)
2cos(2135​)sin(2135−2x​)=0
Divide both sides by 2cos(2135​)2cos(2135​)2cos(2135​)sin(2135−2x​)​=2cos(2135​)0​
Simplifysin(2135−2x​)=0
sin(2135−2x​)=0
General solutions for sin(2135−2x​)=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​​​
2135−2x​=0+2πn,2135−2x​=π+2πn
2135−2x​=0+2πn,2135−2x​=π+2πn
Solve 2135−2x​=0+2πn:x=−2πn+2135​
2135−2x​=0+2πn
0+2πn=2πn2135−2x​=2πn
Multiply both sides by 2
2135−2x​=2πn
Multiply both sides by 222(135−2x)​=2⋅2πn
Simplify135−2x=4πn
135−2x=4πn
Move 135to the right side
135−2x=4πn
Subtract 135 from both sides135−2x−135=4πn−135
Simplify−2x=4πn−135
−2x=4πn−135
Divide both sides by −2
−2x=4πn−135
Divide both sides by −2−2−2x​=−24πn​−−2135​
Simplify
−2−2x​=−24πn​−−2135​
Simplify −2−2x​:x
−2−2x​
Apply the fraction rule: −b−a​=ba​=22x​
Divide the numbers: 22​=1=x
Simplify −24πn​−−2135​:−2πn+2135​
−24πn​−−2135​
−24πn​=−2πn
−24πn​
Apply the fraction rule: −ba​=−ba​=−24πn​
Divide the numbers: 24​=2=−2πn
=−2πn−−2135​
Apply the fraction rule: −ba​=−ba​=−2πn−(−2135​)
Apply rule −(−a)=a=−2πn+2135​
x=−2πn+2135​
x=−2πn+2135​
x=−2πn+2135​
Solve 2135−2x​=π+2πn:x=−π+2135​−2πn
2135−2x​=π+2πn
Multiply both sides by 2
2135−2x​=π+2πn
Multiply both sides by 222(135−2x)​=2π+2⋅2πn
Simplify135−2x=2π+4πn
135−2x=2π+4πn
Move 135to the right side
135−2x=2π+4πn
Subtract 135 from both sides135−2x−135=2π+4πn−135
Simplify−2x=2π+4πn−135
−2x=2π+4πn−135
Divide both sides by −2
−2x=2π+4πn−135
Divide both sides by −2−2−2x​=−22π​+−24πn​−−2135​
Simplify
−2−2x​=−22π​+−24πn​−−2135​
Simplify −2−2x​:x
−2−2x​
Apply the fraction rule: −b−a​=ba​=22x​
Divide the numbers: 22​=1=x
Simplify −22π​+−24πn​−−2135​:−π+2135​−2πn
−22π​+−24πn​−−2135​
Group like terms=−22π​−−2135​+−24πn​
−22π​=−π
−22π​
Apply the fraction rule: −ba​=−ba​=−22π​
Divide the numbers: 22​=1=−π
=−π−−2135​+−24πn​
−2135​=−2135​
−2135​
Apply the fraction rule: −ba​=−ba​=−2135​
−24πn​=−2πn
−24πn​
Apply the fraction rule: −ba​=−ba​=−24πn​
Divide the numbers: 24​=2=−2πn
=−π−(−2135​)−2πn
Apply rule −(−a)=a=−π+2135​−2πn
x=−π+2135​−2πn
x=−π+2135​−2πn
x=−π+2135​−2πn
x=−2πn+2135​,x=−π+2135​−2πn

Graph

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

Popular Examples

tan(x)-4=-14cos^2(x)-8cos(x)+3=0sin(2x)=-0.6(11)/(sin(90))=(10)/(sin(x))2sec^2(x)+4tan(x)=1

Frequently Asked Questions (FAQ)

  • What is the general solution for sin(135-x)=sin(x) ?

    The general solution for sin(135-x)=sin(x) is x=-2pin+135/2 ,x=-pi+135/2-2pin
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