Solve a Trig Equation Linear in Form: 2sin(x)+1=0

Solving a trigonometric equation that is linear in form.

Steps:
Step 1: Isolate the trigonometric function.
Step 2: Determine the reference angle. The reference angle is always an acute angle, so we can use the inverse trigonometric functions of positive ratios.
Step 3: Use the reference angle to find solutions in the appropriate quadrants.
Step 4: Add multiples of the period to the solutions and express answers in terms of an integer n. To express all solutions, add multiples of the period of sine, 2π radians. Let n∈Z.
Step 5: Verify your answers.