I’m unsure how to find this answer. It’s to determine what tan (pi+x) would be after being given the tan x value.

Question

If tan x=3.5, then tan (pi + x) =

Answer 1

tanx = 3.5

x = about 74.055 degrees

add 180 to get 254.055 degrees in the 3rd quadrant

tan 254.055 = 3.5

You could have used the formula tan(A+B) = (tanA + tanB)/(1-tanAtanB) = (3.5 + 0)/(1 -3.5(0))= 3.5/1 = 3.5

tan(pi) = 0 = tan180 degrees

tan(A+B) = sin(A+B))/cos(A+B)

or you might notice tan(x+pi) = tan(x) since pi is the period of the tangent function

Answer 2

Use the tangent angle sum identity:

tan(a+b) = (tan(a)+tan(b))/(1-tan(a)tan(b))

if a = π, then tan(a) = 0

tan(π+x) = (0+tan(x))/(1-0) = tan(x) = 3.5

Answer 3

We have the formula tan(x + y) = (tan(x) + tan(y))/(1 - tan(x)tan(y)) for any angles x and y. We let y = π such that

tan(x + π) = (tan(x) + tan(π))/(1 - tan(x)tan(π))

Since we know that tan(π) = 0, we can simplify such that

tan(x + π) = (tan(x) + 0)/(1 - tan(x)(0))

tan(x + π) = tan(x)

Thus, tan(x + π) = tan(x) is true for all x, so tan(x + π) = 3.5.

Answer 4

tan(π + x) = tanx = 3.5 because π is period for y = tanx