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Popular Trigonometry >

300= 1/32 100^2sin(2x)

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Solution

300=321​1002sin(2x)

Solution

x=21.28700…​+πn,x=2π​−21.28700…​+πn
+1
Degrees
x=36.86989…∘+180∘n,x=53.13010…∘+180∘n
Solution steps
300=321​⋅1002sin(2x)
Switch sides321​⋅1002sin(2x)=300
Simplify 321​⋅1002:2625​
321​⋅1002
Multiply fractions: a⋅cb​=ca⋅b​=321⋅1002​
Multiply: 1⋅1002=1002=321002​
Factor 1002:24⋅54
Factor 100=22⋅52=(22⋅52)2
Apply exponent rule: (ab)c=acbc=(22)2(52)2
Simplify (22)2:24
(22)2
Apply exponent rule: (ab)c=abc=22⋅2
Multiply the numbers: 2⋅2=4=24
Simplify (52)2:54
(52)2
Apply exponent rule: (ab)c=abc=52⋅2
Multiply the numbers: 2⋅2=4=54
=24⋅54
Factor 32:25
Factor 32=25
=2524⋅54​
Cancel 2524⋅54​:254​
2524⋅54​
Apply exponent rule: xbxa​=xb−a1​2524​=25−41​=25−454​
Subtract the numbers: 5−4=1=254​
=254​
54=625=2625​
2625​sin(2x)=300
Multiply both sides by 2
2625​sin(2x)=300
Multiply both sides by 22⋅2625​sin(2x)=300⋅2
Simplify625sin(2x)=600
625sin(2x)=600
Divide both sides by 625
625sin(2x)=600
Divide both sides by 625625625sin(2x)​=625600​
Simplifysin(2x)=2524​
sin(2x)=2524​
Apply trig inverse properties
sin(2x)=2524​
General solutions for sin(2x)=2524​sin(x)=a⇒x=arcsin(a)+2πn,x=π−arcsin(a)+2πn2x=arcsin(2524​)+2πn,2x=π−arcsin(2524​)+2πn
2x=arcsin(2524​)+2πn,2x=π−arcsin(2524​)+2πn
Solve 2x=arcsin(2524​)+2πn:x=2arcsin(2524​)​+πn
2x=arcsin(2524​)+2πn
Divide both sides by 2
2x=arcsin(2524​)+2πn
Divide both sides by 222x​=2arcsin(2524​)​+22πn​
Simplifyx=2arcsin(2524​)​+πn
x=2arcsin(2524​)​+πn
Solve 2x=π−arcsin(2524​)+2πn:x=2π​−2arcsin(2524​)​+πn
2x=π−arcsin(2524​)+2πn
Divide both sides by 2
2x=π−arcsin(2524​)+2πn
Divide both sides by 222x​=2π​−2arcsin(2524​)​+22πn​
Simplifyx=2π​−2arcsin(2524​)​+πn
x=2π​−2arcsin(2524​)​+πn
x=2arcsin(2524​)​+πn,x=2π​−2arcsin(2524​)​+πn
Show solutions in decimal formx=21.28700…​+πn,x=2π​−21.28700…​+πn

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Popular Examples

sin^2(x)= 45/522cos^2(x)-2sin^2(x)=sqrt(3)(pi^2)/8 sec^2((pix)/4)tan((pix)/4)=0sec(x)= 2/3arccos(x)= pi/4

Frequently Asked Questions (FAQ)

  • What is the general solution for 300= 1/32 100^2sin(2x) ?

    The general solution for 300= 1/32 100^2sin(2x) is x=(1.28700…)/2+pin,x= pi/2-(1.28700…)/2+pin
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