# Solve for x in Radians tan(x)^5-9tan(x)=0

Solve for x in Radians tan(x)^5-9tan(x)=0
Factor .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Rewrite as .
Factor.
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Remove unnecessary parentheses.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
Set equal to .
Solve for .
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
The exact value of is .
The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from to find the solution in the fourth quadrant.
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
, for any integer
Set equal to and solve for .
Set equal to .
Solve for .
Subtract from both sides of the equation.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
Simplify .
Rewrite as .
Rewrite as .
Rewrite as .
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set up each of the solutions to solve for .
Solve for in .
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
The inverse tangent of is undefined.
Undefined
Undefined
Solve for in .
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
The inverse tangent of is undefined.
Undefined
Undefined
List all of the solutions.
No solution
No solution
No solution
Set equal to and solve for .
Set equal to .
Solve for .
Add to both sides of the equation.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set up each of the solutions to solve for .
Solve for in .
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
The exact value of is .
The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from to find the solution in the fourth quadrant.
Simplify .
To write as a fraction with a common denominator, multiply by .
Combine fractions.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
Solve for in .
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
The exact value of is .
The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Simplify the expression to find the second solution.
The resulting angle of is positive and coterminal with .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
Add to every negative angle to get positive angles.
Add to to find the positive angle.
To write as a fraction with a common denominator, multiply by .
Combine fractions.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of .
Subtract from .
List the new angles.
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
List all of the solutions.
, for any integer
Consolidate the solutions.
Consolidate and to .
, for any integer
Consolidate and to .
, for any integer
, for any integer
, for any integer
, for any integer
The final solution is all the values that make true.
, for any integer
, for any integer
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### Name

Name two billion eighty-six million nine hundred eighty thousand six hundred nineteen

### Interesting facts

• 2086980619 has 4 divisors, whose sum is 2135515096
• The reverse of 2086980619 is 9160896802
• Previous prime number is 43

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 49
• Digital Root 4

### Name

Name one billion seven hundred forty-three million three hundred ninety-nine thousand six hundred eighty

### Interesting facts

• 1743399680 has 2048 divisors, whose sum is 58492522224
• The reverse of 1743399680 is 0869933471
• Previous prime number is 11

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 50
• Digital Root 5

### Name

Name one hundred six million four hundred ninety-seven thousand sixty-two

### Interesting facts

• 106497062 has 16 divisors, whose sum is 182891520
• The reverse of 106497062 is 260794601
• Previous prime number is 587

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 35
• Digital Root 8