# Trigonometry Examples

Solve for ? tan(x)=-( square root of 3)/3
Step 1
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Step 2
Simplify the right side.
The exact value of is .
Step 3
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.
Step 4
Simplify the expression to find the second solution.
The resulting angle of is positive and coterminal with .
Step 5
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
Step 6
Add to every negative angle to get positive angles.
Add to to find the positive angle.
To write as a fraction with a common denominator, multiply by .
Combine fractions.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of .
Subtract from .
List the new angles.
Step 7
The period of the function is so values will repeat every radians in both directions.
, for any integer
Step 8