# Solve for θ in Degrees tan(theta)^2+6tan(theta)+8=0

Solve for θ in Degrees tan(theta)^2+6tan(theta)+8=0
Factor the left side of the equation.
Let . Substitute for all occurrences of .
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Replace all occurrences of with .
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 .
Subtract from both sides of the equation.
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
Evaluate .
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.
Subtract from .
List the new angles.
The period of the function is so values will repeat every degrees 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 inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
Evaluate .
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.
Subtract from .
List the new angles.
The period of the function is so values will repeat every degrees in both directions.
, for any integer
, for any integer
, for any integer
The final solution is all the values that make true.
, for any integer
Consolidate and to .
, for any integer
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### Name

Name nine hundred forty-eight million seven hundred twenty-three thousand nine hundred

### Interesting facts

• 948723900 has 64 divisors, whose sum is 4098488544
• The reverse of 948723900 is 009327849
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 42
• Digital Root 6

### Name

Name one billion six hundred forty million four hundred sixty-three thousand seventy-eight

### Interesting facts

• 1640463078 has 32 divisors, whose sum is 3487161600
• The reverse of 1640463078 is 8703640461
• Previous prime number is 103

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 39
• Digital Root 3

### Name

Name two hundred twenty-three million two hundred fifty thousand four hundred sixty-nine

### Interesting facts

• 223250469 has 8 divisors, whose sum is 298102080
• The reverse of 223250469 is 964052322
• Previous prime number is 689

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 33
• Digital Root 6