Final answer:
By using the Pythagorean identity, we find sin e to be 0.985, and then we use this value to calculate tan e to be approximately -5.66.
Step-by-step explanation:
The problem you've presented involves finding the value of sin e given that cos e is -0.174, and subsequently using that value to determine tan e. To find sin e, we can use the Pythagorean identity, which states that sin^2 e + cos^2 e = 1. Substituting the given cosine value, we get sin^2 e = 1 - (-0.174)^2. Calculating this yields sin e to be approximately ±0.985. Since cosine is negative and we're working with acute angles in the unit circle, sin e should be positive within the first and second quadrants. Therefore, the correct answer for sin e is (A) 0.985.
To find tan e, which is τ(sin e)/(cos e)τ, we divide the sine value by the cosine value. We compute tan e = 0.985 / -0.174 which yields approximately -5.66, so the correct answer for tan e is (B) -5.66.