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Popular Trigonometry >

sin(θ)=cos(130)

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Solution

sin(θ)=cos(130∘)

Solution

θ=360∘n−40∘,θ=180∘+40∘+360∘n
+1
Radians
θ=−92π​+2πn,θ=π+92π​+2πn
Solution steps
sin(θ)=cos(130∘)
Rewrite using trig identities
cos(130∘)
Use the following identity: cos(x)=sin(90∘−x)sin(90∘−130∘)
sin(θ)=sin(90∘−130∘)
Apply trig inverse properties
sin(θ)=sin(90∘−130∘)
sin(x)=sin(y)⇒x=y+2πn,x=π−y+2πnθ=90∘−130∘+360∘n,θ=180∘−(90∘−130∘)+360∘n
θ=90∘−130∘+360∘n,θ=180∘−(90∘−130∘)+360∘n
θ=90∘−130∘+360∘n:θ=360∘n−40∘
θ=90∘−130∘+360∘n
Simplify 90∘−130∘+360∘n:360∘n−40∘
90∘−130∘+360∘n
Least Common Multiplier of 2,18:18
2,18
Least Common Multiplier (LCM)
Prime factorization of 2:2
2
2 is a prime number, therefore no factorization is possible=2
Prime factorization of 18:2⋅3⋅3
18
18divides by 218=9⋅2=2⋅9
9divides by 39=3⋅3=2⋅3⋅3
2,3 are all prime numbers, therefore no further factorization is possible=2⋅3⋅3
Multiply each factor the greatest number of times it occurs in either 2 or 18=2⋅3⋅3
Multiply the numbers: 2⋅3⋅3=18=18
Adjust Fractions based on the LCM
Multiply each numerator by the same amount needed to multiply its
corresponding denominator to turn it into the LCM 18
For 90∘:multiply the denominator and numerator by 990∘=2⋅9180∘9​=90∘
=90∘−130∘
Since the denominators are equal, combine the fractions: ca​±cb​=ca±b​=18180∘9−2340∘​
Add similar elements: 1620∘−2340∘=−720∘=18−720∘​
Apply the fraction rule: b−a​=−ba​=−40∘
Cancel the common factor: 2=360∘n−40∘
θ=360∘n−40∘
θ=180∘−(90∘−130∘)+360∘n:θ=180∘+40∘+360∘n
θ=180∘−(90∘−130∘)+360∘n
−(90∘−130∘)=40∘
−(90∘−130∘)
Join 90∘−130∘:−40∘
90∘−130∘
Least Common Multiplier of 2,18:18
2,18
Least Common Multiplier (LCM)
Prime factorization of 2:2
2
2 is a prime number, therefore no factorization is possible=2
Prime factorization of 18:2⋅3⋅3
18
18divides by 218=9⋅2=2⋅9
9divides by 39=3⋅3=2⋅3⋅3
2,3 are all prime numbers, therefore no further factorization is possible=2⋅3⋅3
Multiply each factor the greatest number of times it occurs in either 2 or 18=2⋅3⋅3
Multiply the numbers: 2⋅3⋅3=18=18
Adjust Fractions based on the LCM
Multiply each numerator by the same amount needed to multiply its
corresponding denominator to turn it into the LCM 18
For 90∘:multiply the denominator and numerator by 990∘=2⋅9180∘9​=90∘
=90∘−130∘
Since the denominators are equal, combine the fractions: ca​±cb​=ca±b​=18180∘9−2340∘​
Add similar elements: 1620∘−2340∘=−720∘=18−720∘​
Apply the fraction rule: b−a​=−ba​=−40∘
Cancel the common factor: 2=−40∘
=−(−40∘)
Apply rule −(−a)=a=40∘
θ=180∘+40∘+360∘n
θ=360∘n−40∘,θ=180∘+40∘+360∘n

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Popular Examples

3cot(x)+2=5sec^2(x)-tan(x)-1=0cos(x)-sqrt(3)sin(x)=sqrt(2)(cot(θ)+sqrt(3))(csc(θ)+sqrt(2))=0cos(x)=(-2)/5

Frequently Asked Questions (FAQ)

  • What is the general solution for sin(θ)=cos(130) ?

    The general solution for sin(θ)=cos(130) is θ=360n-40,θ=180+40+360n
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