Let tan(x)=2/5 What is the value of tan(2\pi-x)

Question

Let tan(x)=2/5

What is the value of tan(2
`\pi`-x)

Answer 1

Hello from MrBillDoesMath!

Answer:

-2/5

Discussion:

Generally,

tan(2*PI - x ) = - tanx => (*)

and in our case

tan(2*PI - x ) = - tanx = - (2/5) = -2/5

Proof of (*)

tan (2*PI-x) = sin (2*Pi-x)/ cos(2*Pi-x)

Now

sin(2*Pi) * cos(-x) - cos(2*Pi) sin(x) => ( sin(2*PI) = 0, cos(2*Pi) = 1)

= -sin(x)

cos(2*Pi-x) = cos(2*Pi) * cos(-x) + sin(2*Pi)* sin(-x) =>

1 * cos(-x) + 0 =

1 * cos(x) = cos(x)

so tan (2*PI-x) = (-sin(x)) / cos(x) = -tanx

Regards,

MrB