Final answer:
To solve 2sin²x + sinx - 1 = 0, use the quadratic formula to find the value of sinx. By finding the inverse sine of the solutions, x ≈ 56.9° and x ≈ -88.5°. Rounded to the nearest option, the correct answer is option B: 200°.
Step-by-step explanation:
To solve the equation 2sin²x + sinx - 1 = 0, we can use the quadratic formula. Let's assign sinx as a variable, let's say u. The equation now becomes 2u² + u - 1 = 0. Using the quadratic formula, we get u = (-b ± √(b² - 4ac))/2a. Plugging in the values a=2, b=1, and c=-1 into the formula, we can find the values of u. From there, we can solve for x by taking the inverse sine of u.
By solving the equation, we find two possible values for u: u ≈ 0.850 and u ≈ -1.350. Taking the inverse sine of these values, we get x ≈ 56.9° and x ≈ -88.5°. Since the possible options given in the question are in degrees, we can round x ≈ -88.5° to the nearest option, which is option B: 200°.