# Trigonometry Examples

Solve over the Interval square root of 3sec(theta)+2=0 , [0,2pi)
,
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Move the negative in front of the fraction.
Take the inverse secant of both sides of the equation to extract from inside the secant.
The exact value of is .
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 .
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 .
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
Find the values of that produce a value within the interval .
Plug in for and simplify to see if the solution is contained in .
Plug in for .
Simplify.
Multiply .
Multiply by .
Multiply by .
The interval contains .
Plug in for and simplify to see if the solution is contained in .
Plug in for .
Simplify.
Multiply .
Multiply by .
Multiply by .