Trigonometry Examples

Solve over the Interval sec((3theta)/2)=-2 , [0,2pi)
,
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.
Tap for more steps...
Simplify the left side.
Tap for more steps...
Cancel the common factor of .
Tap for more steps...
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply .
Tap for more steps...
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.
Tap for more steps...
Multiply both sides of the equation by .
Simplify both sides of the equation.
Tap for more steps...
Simplify the left side.
Tap for more steps...
Cancel the common factor of .
Tap for more steps...
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Simplify .
Tap for more steps...
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 .
Tap for more steps...
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps...
Multiply by .
Subtract from .
Multiply .
Tap for more steps...
Multiply and .
Multiply by .
Multiply by .
Find the period.
Tap for more steps...
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
Tap for more steps...
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Tap for more steps...
Combine and .
Multiply by .
Combine and .
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 .
Tap for more steps...
Plug in for and simplify to see if the solution is contained in .
Tap for more steps...
Plug in for .
Simplify.
Tap for more steps...
Simplify each term.
Tap for more steps...
Cancel the common factor of and .
Tap for more steps...
Factor out of .
Cancel the common factors.
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply .
Tap for more steps...
Multiply by .
Multiply by .
Add and .
The interval contains .
Plug in for and simplify to see if the solution is contained in .
Tap for more steps...
Plug in for .
Simplify.
Tap for more steps...
Simplify each term.
Tap for more steps...
Cancel the common factor of and .
Tap for more steps...
Factor out of .
Cancel the common factors.
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply .
Tap for more steps...
Multiply by .
Multiply by .
Add and .
The interval contains .
Plug in for and simplify to see if the solution is contained in .
Tap for more steps...
Plug in for .
Simplify.
Tap for more steps...
Multiply by .
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 .
Tap for more steps...
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps...
Multiply by .
Add and .
The interval contains .
Cookies & Privacy
This website uses cookies to ensure you get the best experience on our website.
More Information