Final answer:
Cos(2x) was calculated using the double-angle formula and trigonometric identities, but the correct value does not match any of the provided options.
Step-by-step explanation:
The student's question asks: If sin(x) = 21/22 (in quadrant I), find cos(2x). To find cos(2x), we can use the double-angle formula for cosine, which states cos(2x) = cos2(x) - sin2(x). We already know sin(x) = 21/22, and since the problem is in quadrant I, where all trigonometric functions are positive, we can find cos(x) using the Pythagorean identity sin2(x) + cos2(x) = 1.
First, calculate cos(x):
cos(x) = √(1 - sin2(x)) = √(1 - (21/22)2) = √(1 - 441/484) = √(43/484) = √(43)/22.
Next, apply the double-angle formula:
cos(2x) = cos2(x) - sin2(x) = (√(43)/22)2 - (21/22)2 = 43/484 - 441/484 = -398/484 = -199/242. This answer is not among the provided options, indicating a possible mistake in the options or the question.
Therefore, the provided options do not include the correct value of cos(2x) based on the given sin(x) = 21/22.