use a calculator to solve the equation on the interval 0,2π). sinx = -0.1179 what are the solutions in the…

use a calculator to solve the equation on the interval 0,2π). sinx = -0.1179 what are the solutions in the interval 0,2π)? select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. x = (type your answer in radians. round to four decimal places as needed. use a comma to separate answers as needed.) b. there is no solution.

use a calculator to solve the equation on the interval 0,2π). sinx = -0.1179 what are the solutions in the interval 0,2π)? select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. x = (type your answer in radians. round to four decimal places as needed. use a comma to separate answers as needed.) b. there is no solution.

Answer

Explanation:

Step1: Find the reference angle

Since (\sin x=- 0.1179), the reference angle (x_{ref}=\sin^{-1}(0.1179)). Using a calculator, (x_{ref}\approx0.1182) radians.

Step2: Determine the solutions in the interval ([0,2\pi))

Because (\sin x<0), the solutions are in the third and fourth quadrants. In the third quadrant: (x=\pi + x_{ref}\approx\pi+ 0.1182\approx3.2598) In the fourth quadrant: (x = 2\pi-x_{ref}\approx2\pi - 0.1182\approx6.1650)

Answer:

A. (x = 3.2598,6.1650)