Final answer:
The given information about cos(θ) being -8/17 in the third quadrant does not provide a way to calculate cos(20°) or tan(20°). Trigonometric values of specific angles are generally known or calculated using trigonometric identities, but the provided information isn't applicable in this case.
Step-by-step explanation:
Firstly, there seems to be a typo in the student's question, as cos(0°) = -8/17 is not possible since the cosine of 0 degrees is always 1. However, assuming the student meant a different angle, let's denote it as θ where cos(θ) = -8/17 and this angle θ is in the third quadrant. In the third quadrant, cosine is negative but the question about cos(20°) cannot be directly related to cos(θ) if θ is not explicitly 20° or related by a known identity. Without additional information or context, we cannot calculate cos(20°) or tan(20°) based on the provided information about cos(θ).
Generally, trigonometric values of specific angles like 20 degrees are determined by their definitions on the unit circle or by using trigonometric identities. However, none of the given formulas or information can be directly used to calculate the values for cos(20°) or tan(20°) from cos(θ) because they are not mathematically connected in this context.