Find All Complex Solutions tan(theta)=-2sin(theta)

Math
Move all terms to the left side of the equation and simplify.
Tap for more steps…
Move to the left side of the equation by adding it to both sides.
Rewrite in terms of sines and cosines.
Convert from to .
Rewrite in terms of sines and cosines.
Substitute for .
Factor out of .
Tap for more steps…
Factor out of .
Factor out of .
Factor out of .
Divide each term by and simplify.
Tap for more steps…
Divide each term in by .
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Divide by .
Simplify .
Tap for more steps…
Simplify the denominator.
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.
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Substitute for .
Take the inverse sine of both sides of the equation to extract from inside the sine.
The exact value of is .
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.
Subtract from .
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 .
The period of the function is so values will repeat every radians in both directions.
, for any integer
Consolidate the answers.
, for any integer
Find All Complex Solutions tan(theta)=-2sin(theta)

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top