Approximate the solutions to the following equation on the interval [0,2π). Round your answer to four decimal places.

sinθ=0.65

Apparently, there suppose to be two answers to this question with a comma separating​ both answers. I know because I've failed it and I'm on my 2nd attempt. I literally do not know what this question is and how to go about finding the solution. I don't know where to start. Can someone please show a step-by-step solution. I have 10 more of this sort of questions to solve, so a step-by-step solution would be nice. ​THANKS.

you want the sin⁻¹ function on your calculator

sin⁻¹(0.65) = Θ = .7076 , 2.4340

THANK YOU Scott. I did the reverse sin to get .7076 in my calculator. How did you get 2.4340? Sorry if this question should be obvious to me.

2.4340 = π - .7076

sin(x) is positive in QI and QII

To approximate the solutions to the equation sin(θ) = 0.65 on the interval [0, 2π), you can follow these steps:

Step 1: Start by finding the inverse of the sine function, denoted as sin^(-1) or arcsin.
- On most calculators, this function is represented as "sin^(-1)" or "arcsin." Press the appropriate button on your calculator to access this function.

Step 2: Calculate the arcsin of both sides of the equation sin(θ) = 0.65.
- Take the arcsin of 0.65 on your calculator. The result will be in radians.
- Let's denote this result as a variable, let's say θ1.

Step 3: Find the first solution within the given interval.
- Since the interval is [0, 2π), check if the value of θ1 lies within this range.
- If θ1 is within this range, then it is one of the solutions.

Step 4: Find the second solution within the given interval.
- To find the second solution, add 2π to θ1.
- Let's denote this second solution as θ2.

Step 5: Round the solutions to four decimal places.
- After obtaining θ1 and θ2, round both solutions to four decimal places.

Let's work on an example:

Step 1: Using your calculator, find the arcsin of 0.65.
- arcsin(0.65) ≈ 0.69449 radians

Step 2: We have obtained θ1, which is approximately 0.69449 radians.

Step 3: Check if 0.69449 radians is within the given interval [0, 2π).
- Since 0.69449 is between 0 and 2π (0 < 0.69449 < 2π), it is a valid solution.

Step 4: Find the second solution by adding 2π to θ1.
- θ2 = θ1 + 2π
- θ2 ≈ 0.69449 + 2π ≈ 6.93788 radians

Step 5: Round the solutions to four decimal places.
- Rounded solution for θ1: 0.6945
- Rounded solution for θ2: 6.9379

Therefore, the rounded solutions to the equation sin(θ) = 0.65 on the interval [0, 2π) are approximately 0.6945 and 6.9379 (rounded to four decimal places).