Trigonometry Examples

Solve for ? tan(x)=-1
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
The exact value of is .
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.
Tap for more steps...
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 .
Move the negative in front of the fraction.
Add to .
The resulting angle of is positive and coterminal with .
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...
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.
Tap for more steps...
Add to to find the positive angle.
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...
Move to the left of .
Subtract from .
List the new angles.
The period of the function is so values will repeat every radians in both directions.
, for any integer
Consolidate the answers.
, for any integer
Cookies & Privacy
This website uses cookies to ensure you get the best experience on our website.
More Information