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Popular Trigonometry >

(368.02)/(sin(66-x))=(290)/(sin(38))

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Solution

sin(66∘−x)368.02​=sin(38∘)290​

Solution

x=−360∘n+66∘−0.89673…,x=−180∘−360∘n+66∘+0.89673…
+1
Radians
x=3011π​−0.89673…−2πn,x=−π+3011π​+0.89673…−2πn
Solution steps
sin(66∘−x)368.02​=sin(38∘)290​
Cross multiply
sin(66∘−x)368.02​=sin(38∘)290​
Apply fraction cross multiply: if ba​=dc​ then a⋅d=b⋅c368.02sin(38∘)=sin(66∘−x)⋅290
368.02sin(38∘)=sin(66∘−x)⋅290
Switch sidessin(66∘−x)⋅290=368.02sin(38∘)
Divide both sides by 290
sin(66∘−x)⋅290=368.02sin(38∘)
Divide both sides by 290290sin(66∘−x)⋅290​=290368.02sin(38∘)​
Simplifysin(66∘−x)=290368.02sin(38∘)​
sin(66∘−x)=290368.02sin(38∘)​
Verify Solutions
Find undefined (singularity) points:sin(66∘−x)=0
Take the denominator(s) of sin(66∘−x)368.02​ and compare to zero
sin(66∘−x)=0
The following points are undefinedsin(66∘−x)=0
Combine undefined points with solutions:
sin(66∘−x)=290368.02sin(38∘)​
Apply trig inverse properties
sin(66∘−x)=290368.02sin(38∘)​
General solutions for sin(66∘−x)=290368.02sin(38∘)​sin(x)=a⇒x=arcsin(a)+360∘n,x=180∘−arcsin(a)+360∘n66∘−x=arcsin(290368.02sin(38∘)​)+360∘n,66∘−x=180∘−arcsin(290368.02sin(38∘)​)+360∘n
66∘−x=arcsin(290368.02sin(38∘)​)+360∘n,66∘−x=180∘−arcsin(290368.02sin(38∘)​)+360∘n
Solve 66∘−x=arcsin(290368.02sin(38∘)​)+360∘n:x=−360∘n+66∘−arcsin(290368.02sin(38∘)​)
66∘−x=arcsin(290368.02sin(38∘)​)+360∘n
Move 66∘to the right side
66∘−x=arcsin(290368.02sin(38∘)​)+360∘n
Subtract 66∘ from both sides66∘−x−66∘=arcsin(290368.02sin(38∘)​)+360∘n−66∘
Simplify−x=arcsin(290368.02sin(38∘)​)+360∘n−66∘
−x=arcsin(290368.02sin(38∘)​)+360∘n−66∘
Divide both sides by −1
−x=arcsin(290368.02sin(38∘)​)+360∘n−66∘
Divide both sides by −1−1−x​=−1arcsin(290368.02sin(38∘)​)​+−1360∘n​−−166∘​
Simplify
−1−x​=−1arcsin(290368.02sin(38∘)​)​+−1360∘n​−−166∘​
Simplify −1−x​:x
−1−x​
Apply the fraction rule: −b−a​=ba​=1x​
Apply rule 1a​=a=x
Simplify −1arcsin(290368.02sin(38∘)​)​+−1360∘n​−−166∘​:−360∘n+66∘−arcsin(290368.02sin(38∘)​)
−1arcsin(290368.02sin(38∘)​)​+−1360∘n​−−166∘​
Group like terms=−1360∘n​−−166∘​+−1arcsin(290368.02sin(38∘)​)​
−1360∘n​=−360∘n
−1360∘n​
Apply the fraction rule: −ba​=−ba​=−1360∘n​
Apply rule 1a​=a=−360∘n
=−360∘n−−166∘​+−1arcsin(290368.02sin(38∘)​)​
−166∘​=−66∘
−166∘​
Apply the fraction rule: −ba​=−ba​=−166∘​
Apply the fraction rule: 1a​=a166∘​=66∘=−66∘
−1arcsin(290368.02sin(38∘)​)​=−arcsin(290368.02sin(38∘)​)
−1arcsin(290368.02sin(38∘)​)​
Apply the fraction rule: −ba​=−ba​=−1arcsin(290368.02sin(38∘)​)​
Apply the fraction rule: 1a​=a1arcsin(290368.02sin(38∘)​)​=arcsin(290368.02sin(38∘)​)=−arcsin(290368.02sin(38∘)​)
=−360∘n−(−66∘)−arcsin(290368.02sin(38∘)​)
Apply rule −(−a)=a=−360∘n+66∘−arcsin(290368.02sin(38∘)​)
x=−360∘n+66∘−arcsin(290368.02sin(38∘)​)
x=−360∘n+66∘−arcsin(290368.02sin(38∘)​)
x=−360∘n+66∘−arcsin(290368.02sin(38∘)​)
Solve 66∘−x=180∘−arcsin(290368.02sin(38∘)​)+360∘n:x=−180∘−360∘n+66∘+arcsin(290368.02sin(38∘)​)
66∘−x=180∘−arcsin(290368.02sin(38∘)​)+360∘n
Move 66∘to the right side
66∘−x=180∘−arcsin(290368.02sin(38∘)​)+360∘n
Subtract 66∘ from both sides66∘−x−66∘=180∘−arcsin(290368.02sin(38∘)​)+360∘n−66∘
Simplify−x=180∘−arcsin(290368.02sin(38∘)​)+360∘n−66∘
−x=180∘−arcsin(290368.02sin(38∘)​)+360∘n−66∘
Divide both sides by −1
−x=180∘−arcsin(290368.02sin(38∘)​)+360∘n−66∘
Divide both sides by −1−1−x​=−1180∘​−−1arcsin(290368.02sin(38∘)​)​+−1360∘n​−−166∘​
Simplify
−1−x​=−1180∘​−−1arcsin(290368.02sin(38∘)​)​+−1360∘n​−−166∘​
Simplify −1−x​:x
−1−x​
Apply the fraction rule: −b−a​=ba​=1x​
Apply rule 1a​=a=x
Simplify −1180∘​−−1arcsin(290368.02sin(38∘)​)​+−1360∘n​−−166∘​:−180∘−360∘n+66∘+arcsin(290368.02sin(38∘)​)
−1180∘​−−1arcsin(290368.02sin(38∘)​)​+−1360∘n​−−166∘​
Group like terms=−1180∘​+−1360∘n​−−166∘​−−1arcsin(290368.02sin(38∘)​)​
−1180∘​=−180∘
−1180∘​
Apply the fraction rule: −ba​=−ba​=−180∘
Apply rule 1a​=a=−180∘
=−180∘+−1360∘n​−−166∘​−−1arcsin(290368.02sin(38∘)​)​
−1360∘n​=−360∘n
−1360∘n​
Apply the fraction rule: −ba​=−ba​=−1360∘n​
Apply rule 1a​=a=−360∘n
=−180∘−360∘n−−166∘​−−1arcsin(290368.02sin(38∘)​)​
−166∘​=−66∘
−166∘​
Apply the fraction rule: −ba​=−ba​=−166∘​
Apply the fraction rule: 1a​=a166∘​=66∘=−66∘
−1arcsin(290368.02sin(38∘)​)​=−arcsin(290368.02sin(38∘)​)
−1arcsin(290368.02sin(38∘)​)​
Apply the fraction rule: −ba​=−ba​=−1arcsin(290368.02sin(38∘)​)​
Apply the fraction rule: 1a​=a1arcsin(290368.02sin(38∘)​)​=arcsin(290368.02sin(38∘)​)=−arcsin(290368.02sin(38∘)​)
=−180∘−360∘n−(−66∘)−(−arcsin(290368.02sin(38∘)​))
Apply rule −(−a)=a=−180∘−360∘n+66∘+arcsin(290368.02sin(38∘)​)
x=−180∘−360∘n+66∘+arcsin(290368.02sin(38∘)​)
x=−180∘−360∘n+66∘+arcsin(290368.02sin(38∘)​)
x=−180∘−360∘n+66∘+arcsin(290368.02sin(38∘)​)
x=−360∘n+66∘−arcsin(290368.02sin(38∘)​),x=−180∘−360∘n+66∘+arcsin(290368.02sin(38∘)​)
Show solutions in decimal formx=−360∘n+66∘−0.89673…,x=−180∘−360∘n+66∘+0.89673…

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