Use a calculator to approximate two values of theta (0 <= theta < 2pi) if csc theta = 1.03. Round answer to two decimal places.
To approximate values of theta in this case, we need to use the inverse of the csc function, which is the arcsin function. However, typical calculators do not have an arcsin button but instead have a sin button. We can use this sin function to find theta.
To solve for theta, we can use the following steps:
1. Take the reciprocal of csc theta to get sin theta. Since csc theta = 1.03, sin theta = 1 / 1.03 ≈ 0.970.
2. Enter the sin button on your calculator (usually represented as "sin" or "sin^-1") and input the value you obtained in step 1 (0.970).
3. Press the "=" button to get the value of theta. This will give you the first value of theta.
Next, we need to find the second value of theta. Since the sine function is periodic, we can add 2π (approximately 6.28) to the first value of theta to get the second value.
4. Add 2π (approximately 6.28) to the first value of theta you obtained in step 3.
5. Press the "=" button to get the value of the second theta.
After following these steps, you should have two approximations for theta, rounded to two decimal places.