Solve the equation. Give a general formula for all the solutions. List six solutions.
Sin\left(2\theta \right)=-\frac{1}{2}
Write the general formula for all the solutions to sine left parenthesis 2 theta right parenthesis equals negative one half
based on the smaller angle.
thetaequals
enter your response here
(Simplify your answer. Use angle measures greater than or equal to 0 and less than pi. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the expression. Type an expression using k as the variable.)
Part 2
Write the general formula for all the solutions to sine left parenthesis 2 theta right parenthesis equals negative one half
based on the larger angle.
thetaequals
enter your response here
(Simplify your answer. Use angle measures greater than or equal to 0 and less than pi. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the expression. Type an expression using k as the variable.)
Part 3
List the first six solutions that are greater than or equal to 0.
thetaequals
enter your response here
(Simplify your answer. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
Part 1:
The general formula for all the solutions based on the smaller angle is:
θ = (2k + 1)π/6, where k is an integer.
Part 2:
The general formula for all the solutions based on the larger angle is:
θ = (2k + 1)π/6 + π, where k is an integer.
Part 3:
The first six solutions that are greater than or equal to 0 are:
θ = π/6, 5π/6, 7π/6, 11π/6, 13π/6, 17π/6