Domain Of A Tangent Function Math

The period of the function is 360 or 2π radians.

Domain of a tangent function math. There is no worse ii for inverse tangent. The domain for the parent function of tangent does not exist for. The tangent function is a periodic function which is very important in trigonometry. This can be written as θ r.

All real numbers r except pi 2 k pi k is an integer. If you mean a tangent as in the tangent line of some function math f math at some point math x 0 math then that line can be parametrized by for example math g t f x 0 f x 0 t math in doing so the domain of math g math is the whole real line math mathbb r math. Tan x domain of tangent. Range of tangent period of tangent and other properties.

But if you choose the function math g s g tan s math for math frac pi 2 s frac pi 2 math the image of math g math is also the same whole tangent line but in this case the domain is. The simplest way to understand the tangent function is to use the unit circle. The shape of the tangent curve is the same for each full rotation of the angle and so the function is called periodic. As you drag the point a around notice that after a full rotation about b the graph shape repeats.

Below is a graph of y tan x showing 3 periods of tangent. In reference to the coordinate plane tangent is y x and cotangent is x y. 4 10 2009 7 51 06 am. Domain range and de nition of the three main inverse trigonometric functions.

The amplitude and the vertical shift will not affect the domain or the period of the graph. Undefined control sequence textup. The domain of the tangent function has holes in it. The domains of both functions are restricted because sometimes their ratios could have zeros in the denominator but their ranges are infinite.

X k pi place k is an integer. The tells us that the graph will shift right units. Only good ii and bad ii. Undefined control sequence textup.

The tangent and cotangent are related not only by the fact that they re reciprocals but also by the behavior of their ranges. The domain of tangent so tangent domain so the domain is essentially all real numbers all reals except multiples of pi over i guess you can say pi over two plus multiples of pi except pi over two plus multiples of pi where k could be any integer so you could also be subtracting pi because if you have pi over two if you add pi you go straight down here.