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Popular Trigonometry >

sin(-pi/8 c)=-14/14

  • Pre Algebra
  • Algebra
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Solution

sin(−8π​c)=−1414​

Solution

c=−12−16n
+1
Degrees
c=−687.54935…∘−916.73247…∘n
Solution steps
sin(−8π​c)=−1414​
Apply rule aa​=1sin(−8π​c)=−1
General solutions for sin(−8π​c)=−1
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​​​
−8π​c=23π​+2πn
−8π​c=23π​+2πn
Solve −8π​c=23π​+2πn:c=−12−16n
−8π​c=23π​+2πn
Multiply both sides by 8
−8π​c=23π​+2πn
Multiply both sides by 88(−8π​c)=8⋅23π​+8⋅2πn
Simplify
8(−8π​c)=8⋅23π​+8⋅2πn
Simplify 8(−8π​c):−πc
8(−8π​c)
Remove parentheses: (−a)=−a=−8⋅8π​c
Multiply fractions: a⋅cb​=ca⋅b​=−88π​c
Cancel the common factor: 8=−cπ
Simplify 8⋅23π​+8⋅2πn:12π+16πn
8⋅23π​+8⋅2πn
8⋅23π​=12π
8⋅23π​
Multiply fractions: a⋅cb​=ca⋅b​=23π8​
Multiply the numbers: 3⋅8=24=224π​
Divide the numbers: 224​=12=12π
8⋅2πn=16πn
8⋅2πn
Multiply the numbers: 8⋅2=16=16πn
=12π+16πn
−πc=12π+16πn
−πc=12π+16πn
−πc=12π+16πn
Divide both sides by −π
−πc=12π+16πn
Divide both sides by −π−π−πc​=−π12π​+−π16πn​
Simplify
−π−πc​=−π12π​+−π16πn​
Simplify −π−πc​:c
−π−πc​
Apply the fraction rule: −b−a​=ba​=ππc​
Cancel the common factor: π=c
Simplify −π12π​+−π16πn​:−12−16n
−π12π​+−π16πn​
−π12π​=−12
−π12π​
Apply the fraction rule: −ba​=−ba​=−π12π​
Cancel the common factor: π=−12
=−12+−π16πn​
−π16πn​=−16n
−π16πn​
Apply the fraction rule: −ba​=−ba​=−π16πn​
Cancel the common factor: π=−16n
=−12−16n
c=−12−16n
c=−12−16n
c=−12−16n
c=−12−16n

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Frequently Asked Questions (FAQ)

  • What is the general solution for sin(-pi/8 c)=-14/14 ?

    The general solution for sin(-pi/8 c)=-14/14 is c=-12-16n
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