Trigonometry Examples

Solve for B in Degrees 12tan(B)+5=5tan(B)+5
Step 1
Move all terms containing to the left side of the equation.
Tap for more steps...
Step 1.1
Subtract from both sides of the equation.
Step 1.2
Subtract from .
Step 2
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 2.1
Subtract from both sides of the equation.
Step 2.2
Subtract from .
Step 3
Divide each term in by and simplify.
Tap for more steps...
Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
Tap for more steps...
Step 3.2.1
Cancel the common factor of .
Tap for more steps...
Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Divide by .
Step 3.3
Simplify the right side.
Tap for more steps...
Step 3.3.1
Divide by .
Step 4
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Step 5
Simplify the right side.
Tap for more steps...
Step 5.1
The exact value of is .
Step 6
The tangent function is positive in the first and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Step 7
Add and .
Step 8
Find the period of .
Tap for more steps...
Step 8.1
The period of the function can be calculated using .
Step 8.2
Replace with in the formula for period.
Step 8.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 8.4
Divide by .
Step 9
The period of the function is so values will repeat every degrees in both directions.
, for any integer
Step 10
Consolidate the answers.
, for any integer