Solve for x sec((3x)/2)=-2

Solve for x sec((3x)/2)=-2
Take the inverse secant of both sides of the equation to extract from inside the secant.
The exact value of is .
Multiply both sides of the equation by .
Simplify both sides of the equation.
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply .
Multiply and .
Multiply by .
Multiply by .
The secant function is negative in the second and third 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.
Multiply both sides of the equation by .
Simplify both sides of the equation.
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Simplify .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Multiply .
Multiply and .
Multiply by .
Multiply by .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Combine and .
Multiply by .
Combine and .
The period of the function is so values will repeat every radians in both directions.
, for any integer
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Name

Name thirty-six million eight hundred ninety-five thousand six hundred forty-seven

Interesting facts

• 36895647 has 8 divisors, whose sum is 49887360
• The reverse of 36895647 is 74659863
• Previous prime number is 71

Basic properties

• Is Prime? no
• Number parity odd
• Number length 8
• Sum of Digits 48
• Digital Root 3

Name

Name one billion four hundred nine million seven hundred fifty-six thousand three hundred eighteen

Interesting facts

• 1409756318 has 8 divisors, whose sum is 2123483040
• The reverse of 1409756318 is 8136579041
• Previous prime number is 239

Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 44
• Digital Root 8

Name

Name one billion nine hundred seventy-seven million five hundred eighty-eight thousand two hundred fifty-seven

Interesting facts

• 1977588257 has 4 divisors, whose sum is 2093916996
• The reverse of 1977588257 is 7528857791
• Previous prime number is 17

Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 59
• Digital Root 5