Final answer:
The exact value of cos(570°) is found by considering the periodicity of the cosine function and simplifying to cos(210°), which is -√3/2. There's no match among the provided options.
Step-by-step explanation:
The question asks to find the exact value of cos(570°). To find this, we can use the fact that the cosine function is periodic with a period of 360°. Therefore, cos(570°) is equivalent to cos(570° - 360°), which simplifies to cos(210°). The cosine of 210° is in the third quadrant where the cosine values are negative, and since 210° is 30° more than 180°, cos(210°) = -cos(30°). The cosine of 30° is √3/2, so cos(210°) = -√3/2. Therefore, the exact value of cos(570°) is -cos(30°) or -√3/2, which is none of the provided options A, B, C, or D.