To solve for sin(θ) given the conditions, let’s first clarify what we know:
- cos(5) = 13: This part of the statement is not clear as the cosine function ranges from -1 to 1. Such a value is not valid in the context of trigonometric functions.
- tan(θ) = 0: The tangent of an angle is zero when the sine of that angle is zero. This occurs at angles where θ is a multiple of π (i.e., 0, π, 2π, …).
Given the valid part of the statement that tan(θ) = 0, we can conclude:
- sin(θ) = 0: Since tan(θ) = sin(θ) / cos(θ), having tan(θ) = 0 directly implies that sin(θ) = 0, irrespective of the value of cos(θ) (as long as it’s not also zero).
In summary, regardless of the cosine value provided (which seems incorrect), the important takeaway is that if tan(θ) = 0, then sin(θ) must equal 0.