Final answer:
To find the exact trigonometric values for the given angles, we use reference angles and trigonometric identities. The correct values for 75° and the reference angle of 1659° are sine: 0.2588, cosine: 0.9659, and tangent: 3.7321.
Step-by-step explanation:
To find the exact value of the sine, cosine, and tangent for the angles given, we need to make sure that the angles are in the standard position (between 0° and 360°) or use their reference angles to find the exact values. For an angle like 75°, these values can be found by using the sum of angles formula, as 75° is not a standard angle. However, given the options provided, we must identify which option presents the correct sine, cosine, and tangent values for the given angles of 75° and 1659°.
First, we need to find the reference angle for 1659°. We do this by dividing the angle by 360 and taking the remainder, which gives us a reference angle of 159°. Now, considering that 159° is in the second quadrant where sine is positive and cosine and tangent are negative, we can rule out the options that do not match this criterion.
After analyzing the reference angles and corresponding trigonometric values, the correct answer is: Sine: 0.2588, Cosine: 0.9659, Tangent: 3.7321 which makes the correct option C.