Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 8 sin(2θ) − 2 sin(θ) = 0

Step-by-step explanation:

Factor constant terms:

Divide both sides by -2:

Expand trigonometric functions using the fact:

So:

Factor sin(x) and constant terms and multiply both sides by -1:

Split into two equations:

For (1)

Add 1 to both sides and divide both sides by 8:

Take the inverse cosine of both sides:

For (2)

Simply take the inverse sine of both sides

Therefore, the solutions are given by:

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice