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Popular Trigonometry >

tan((3θ)/4)=(-sqrt(3))/3

  • Pre Algebra
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Solution

tan(43θ​)=3−3​​

Solution

θ=910π​+34πn​
+1
Degrees
θ=200∘+240∘n
Solution steps
tan(43θ​)=3−3​​
Apply the fraction rule: b−a​=−ba​tan(43θ​)=−33​​
General solutions for tan(43θ​)=−33​​
tan(x) periodicity table with πn cycle:
x06π​4π​3π​2π​32π​43π​65π​​tan(x)033​​13​±∞−3​−1−33​​​​
43θ​=65π​+πn
43θ​=65π​+πn
Solve 43θ​=65π​+πn:θ=910π​+34πn​
43θ​=65π​+πn
Multiply both sides by 4
43θ​=65π​+πn
Multiply both sides by 444⋅3θ​=4⋅65π​+4πn
Simplify
44⋅3θ​=4⋅65π​+4πn
Simplify 44⋅3θ​:3θ
44⋅3θ​
Multiply the numbers: 4⋅3=12=412θ​
Divide the numbers: 412​=3=3θ
Simplify 4⋅65π​+4πn:310π​+4πn
4⋅65π​+4πn
4⋅65π​=310π​
4⋅65π​
Multiply fractions: a⋅cb​=ca⋅b​=65π4​
Multiply the numbers: 5⋅4=20=620π​
Cancel the common factor: 2=310π​
=310π​+4πn
3θ=310π​+4πn
3θ=310π​+4πn
3θ=310π​+4πn
Divide both sides by 3
3θ=310π​+4πn
Divide both sides by 333θ​=3310π​​+34πn​
Simplify
33θ​=3310π​​+34πn​
Simplify 33θ​:θ
33θ​
Divide the numbers: 33​=1=θ
Simplify 3310π​​+34πn​:910π​+34πn​
3310π​​+34πn​
3310π​​=910π​
3310π​​
Apply the fraction rule: acb​​=c⋅ab​=3⋅310π​
Multiply the numbers: 3⋅3=9=910π​
=910π​+34πn​
θ=910π​+34πn​
θ=910π​+34πn​
θ=910π​+34πn​
θ=910π​+34πn​

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Popular Examples

30=15cos((2pi)/(365)t)+43sin(x)=+1esin(2x)cos(x)+cos(2x)sin(x)=-12cos(x)=0.2cos(a)=-sin(a)

Frequently Asked Questions (FAQ)

  • What is the general solution for tan((3θ)/4)=(-sqrt(3))/3 ?

    The general solution for tan((3θ)/4)=(-sqrt(3))/3 is θ=(10pi)/9+(4pin)/3
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