What Are All Solution of Tan 2x 3
Trigonometry Examples
Add to both sides of the equation.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set up each of the solutions to solve for .
Set up the equation to solve for .
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Divide each term by and simplify.
Reduce the expression by cancelling the common factors.
Cancel the common factor.
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.
Simplify the expression to find the second solution.
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 .
Combine the numerators over the common denominator.
Move to the left of the expression .
Divide each term by and simplify.
Reduce the expression by cancelling the common factors.
Cancel the common factor.
Cancel the common factor of .
Factor out the greatest common factor .
Cancel the common factor.
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 .
The period of the function is so values will repeat every radians in both directions.
, for any integer
Consolidate the answers.
, for any integer
Set up the equation to solve for .
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Divide each term by and simplify.
Reduce the expression by cancelling the common factors.
Cancel the common factor.
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.
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 .
Combine the numerators over the common denominator.
Move the negative in front of the fraction.
Divide each term by and simplify.
Reduce the expression by cancelling the common factors.
Cancel the common factor.
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out the greatest common factor .
Cancel the common factor.
Move the negative in front of the fraction.
The resulting angle of is positive and coterminal with .
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 .
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 .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine the numerators over the common denominator.
Move to the left of the expression .
Reduce the expression by cancelling the common factors.
Cancel the common factors.
Cancel the common factor.
The period of the function is so values will repeat every radians in both directions.
, for any integer
Consolidate the answers.
, for any integer
List all of the results found in the previous steps.
, for any integer
What Are All Solution of Tan 2x 3
Source: https://www.mathway.com/popular-problems/Trigonometry/319846
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