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Popular Trigonometry >

2cos(12x)=sqrt(3)

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Solution

2cos(12x)=3​

Solution

x=72π​+6πn​,x=7211π​+6πn​
+1
Degrees
x=2.5∘+30∘n,x=27.5∘+30∘n
Solution steps
2cos(12x)=3​
Divide both sides by 2
2cos(12x)=3​
Divide both sides by 222cos(12x)​=23​​
Simplifycos(12x)=23​​
cos(12x)=23​​
General solutions for cos(12x)=23​​
cos(x) periodicity table with 2πn cycle:
x06π​4π​3π​2π​32π​43π​65π​​cos(x)123​​22​​21​0−21​−22​​−23​​​xπ67π​45π​34π​23π​35π​47π​611π​​cos(x)−1−23​​−22​​−21​021​22​​23​​​​
12x=6π​+2πn,12x=611π​+2πn
12x=6π​+2πn,12x=611π​+2πn
Solve 12x=6π​+2πn:x=72π​+6πn​
12x=6π​+2πn
Divide both sides by 12
12x=6π​+2πn
Divide both sides by 121212x​=126π​​+122πn​
Simplify
1212x​=126π​​+122πn​
Simplify 1212x​:x
1212x​
Divide the numbers: 1212​=1=x
Simplify 126π​​+122πn​:72π​+6πn​
126π​​+122πn​
126π​​=72π​
126π​​
Apply the fraction rule: acb​​=c⋅ab​=6⋅12π​
Multiply the numbers: 6⋅12=72=72π​
122πn​=6πn​
122πn​
Cancel the common factor: 2=6πn​
=72π​+6πn​
x=72π​+6πn​
x=72π​+6πn​
x=72π​+6πn​
Solve 12x=611π​+2πn:x=7211π​+6πn​
12x=611π​+2πn
Divide both sides by 12
12x=611π​+2πn
Divide both sides by 121212x​=12611π​​+122πn​
Simplify
1212x​=12611π​​+122πn​
Simplify 1212x​:x
1212x​
Divide the numbers: 1212​=1=x
Simplify 12611π​​+122πn​:7211π​+6πn​
12611π​​+122πn​
12611π​​=7211π​
12611π​​
Apply the fraction rule: acb​​=c⋅ab​=6⋅1211π​
Multiply the numbers: 6⋅12=72=7211π​
122πn​=6πn​
122πn​
Cancel the common factor: 2=6πn​
=7211π​+6πn​
x=7211π​+6πn​
x=7211π​+6πn​
x=7211π​+6πn​
x=72π​+6πn​,x=7211π​+6πn​

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Popular Examples

7sin(5x)=2arccot(x)+arccot(1+x)= pi/4arcsin(x-0.355)=0.489cos(pi/2-x)= 4/56=10cos(4*o)

Frequently Asked Questions (FAQ)

  • What is the general solution for 2cos(12x)=sqrt(3) ?

    The general solution for 2cos(12x)=sqrt(3) is x= pi/(72)+(pin)/6 ,x=(11pi}{72}+\frac{pin)/6
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