Question

If F(theta)=tan theta=3, find F(theta+pi)

Answer 1

As given

`f(\theta) = tan( \theta) = 3`

So
`f(\theta + \pi) = tan (\theta + \pi)`

And we know
`tan(\theta + \pi) = -tan(\theta)` because it is in second quadrant and tan is negative in second quadrant.

So
`f(\theta + \pi) = -tan(\theta) = -3`

So answer is -3.

Answer 2

Given:
f(θ) = tan(θ) = 3

Note that

`tan(x+y) = (tanx + tany)/(1-tanx \, tany)`

Note that tan(π) = 0.
Therefore
f(θ + π) = tan(θ+π)
= (tanθ + tan π)/(1 -tanθ tan π)
= 3/1 = 3

Answer: 3