How do you find the tangent if the cosine is one divided by four times the sine?

To find the tangent when given the relationship that cosine is one divided by four times the sine, we can start by defining the terms mathematically.

We know that:

tan(θ) = sin(θ) / cos(θ)

According to the problem, we have:

cos(θ) = (1/4) * sin(θ)

We can rewrite this in terms of tangent:

tan(θ) = sin(θ) / ((1/4) * sin(θ))

This simplifies as follows:

tan(θ) = sin(θ) / (1/4 * sin(θ)) = 4

So, the tangent of the angle (θ) is equal to:

tan(θ) = 4

In conclusion, given that cosine is one divided by four times the sine, the value of the tangent is 4. This relationship illustrates how we can manipulate trigonometric identities to find tangential values based on other trigonometric functions.