Enter a problem...
Trigonometry Examples
Step 1
Substitute for .
Step 2
Add to both sides of the equation.
Step 3
Subtract from both sides of the equation.
Step 4
Use the quadratic formula to find the solutions.
Step 5
Substitute the values , , and into the quadratic formula and solve for .
Step 6
Step 6.1
Simplify the numerator.
Step 6.1.1
Raise to the power of .
Step 6.1.2
Multiply .
Step 6.1.2.1
Multiply by .
Step 6.1.2.2
Multiply by .
Step 6.1.3
Add and .
Step 6.1.4
Rewrite as .
Step 6.1.4.1
Factor out of .
Step 6.1.4.2
Rewrite as .
Step 6.1.5
Pull terms out from under the radical.
Step 6.2
Multiply by .
Step 6.3
Simplify .
Step 7
The final answer is the combination of both solutions.
Step 8
Substitute for .
Step 9
Set up each of the solutions to solve for .
Step 10
Step 10.1
Convert the right side of the equation to its decimal equivalent.
Step 10.2
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Step 10.3
Simplify the right side.
Step 10.3.1
Evaluate .
Step 10.4
The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from to find the solution in the fourth quadrant.
Step 10.5
Solve for .
Step 10.5.1
Remove parentheses.
Step 10.5.2
Remove parentheses.
Step 10.5.3
Add and .
Step 10.6
Find the period of .
Step 10.6.1
The period of the function can be calculated using .
Step 10.6.2
Replace with in the formula for period.
Step 10.6.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 10.6.4
Divide by .
Step 10.7
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
Step 11
Step 11.1
Convert the right side of the equation to its decimal equivalent.
Step 11.2
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Step 11.3
Simplify the right side.
Step 11.3.1
Evaluate .
Step 11.4
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 11.5
Simplify the expression to find the second solution.
Step 11.5.1
Add to .
Step 11.5.2
The resulting angle of is positive and coterminal with .
Step 11.6
Find the period of .
Step 11.6.1
The period of the function can be calculated using .
Step 11.6.2
Replace with in the formula for period.
Step 11.6.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 11.6.4
Divide by .
Step 11.7
Add to every negative angle to get positive angles.
Step 11.7.1
Add to to find the positive angle.
Step 11.7.2
Replace with decimal approximation.
Step 11.7.3
Subtract from .
Step 11.7.4
List the new angles.
Step 11.8
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
Step 12
List all of the solutions.
, for any integer
Step 13
Step 13.1
Consolidate and to .
, for any integer
Step 13.2
Consolidate and to .
, for any integer
, for any integer