Final answer:
Without the original function's context, we can't determine the exact equation for the tangent line at θ = π/6. Assuming a right triangle, the slope of the tangent would be √3. Options a) and b) match this slope, but we cannot identify the correct y-intercept without additional information.
Step-by-step explanation:
To find the equation of the tangent line at θ = π/6, we need to establish which curve or function we are dealing with so we can differentiate it. However, the question does not specify the original function to which the tangent line belongs. Without the necessary context or function, it's not possible to calculate the derivative or determine the tangent line's equation. Nevertheless, if we assume the question wants us to look at the tangent function for a right triangle, then we can use the properties of a right triangle at θ = π/6 where the tangent (opposite/adjacent) is √3/1. Thus, the slope of the tangent line would be √3. The y-intercept cannot be determined without additional information. From the options provided:
- y = √3x - 1
- y = √3x + 1
- y = -√3x - 1
- y = -√3x + 1
The options that match the slope √3 are a) and b). Without the y-intercept, we cannot choose between them based on the information given in the question.