# Solve for x 1/(cos(x))=8/3

Solve for x 1/(cos(x))=8/3
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
Solve the equation for .
Rewrite the equation as .
Multiply by .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Evaluate .
The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Simplify .
Multiply by .
Subtract from .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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
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