Solve for ? cos(2theta)=11sin(theta)-5

Math
Factor by grouping.
Tap for more steps…
Reorder terms.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Tap for more steps…
Factor out of .
Rewrite as plus
Apply the distributive property.
Multiply by .
Factor out the greatest common factor from each group.
Tap for more steps…
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Tap for more steps…
Set the first factor equal to .
Add to both sides of the equation.
Multiply each term in by
Tap for more steps…
Multiply each term in by .
Multiply .
Tap for more steps…
Multiply by .
Multiply by .
Multiply by .
The range of sine is . Since does not fall in this range, there is no solution.
No solution
No solution
Set the next factor equal to and solve.
Tap for more steps…
Set the next factor equal to .
Add to both sides of the equation.
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 .
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.
Simplify .
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.
Simplify the numerator.
Tap for more steps…
Move to the left of .
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
, for any integer
The final solution is all the values that make true.
, for any integer
Solve for ? cos(2theta)=11sin(theta)-5

Download our
App from the store

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

Scroll to top