rewrite tan(sin^-14v) as an algebraic expression in v
To rewrite tan(sin^(-1)(4v)) as an algebraic expression in v, we need to first understand the inverse trigonometric function sin^(-1)(x), which is also commonly denoted as arcsin(x).
The inverse trigonometric function sin^(-1)(x) represents the angle whose sine is equal to x. In other words, if sin^(-1)(x) = θ, then sin(θ) = x.
Now, let's apply this information to the given expression:
tan(sin^(-1)(4v))
Using the inverse trigonometric function sin^(-1)(4v), we can find the angle whose sine is equal to 4v, denoting it as θ:
sin^(-1)(4v) = θ
Now, we need to find the tangent of this angle θ:
tan(θ)
Since we have θ = sin^(-1)(4v), we can substitute it into the expression:
tan(sin^(-1)(4v))
Therefore, the algebraic expression for tan(sin^(-1)(4v)) is tan(θ), where θ = sin^(-1)(4v).
assuming you meant arcsin(14v), think of the triangle with leg 4v and hypotenuse 1.
The other leg is √(1-16v^2), so
tan arcsin(4v) = 4v/√(1-16v^2)