Answer:
223° and 317°
Explanation:
To find the values of x for which sin x = -0.6745, we can use the inverse sine function (sin^-1) on a calculator:
sin^-1 (-0.6745) = -43.01° or -136.99° (rounded to two decimal places)
However, since the question specifies that x is in the interval 0° < x < 360°, we need to adjust our answer to fit within that range.
For the first solution, we can add 360° to get:
-43.01° + 360° = 316.99°
Therefore, one solution is x = 317° (rounded to the nearest degree).
For the second solution, we can subtract from 360° to get:
360° - 136.99° = 223.01°
Therefore, another solution is x = 223° (rounded to the nearest degree).
Thus, the values of x for which sin x = -0.6745 within the interval 0° < x < 360° are approximately 223° and 317°.