# Trigonometry

posted by Betty

What is the period and asymptote in y= tan(2x-pi)

1. Reiny

for y = tan kØ , the period of the tangent curve is π/k
(notice that this differs from the period definition for sine and cosine)

so the period of tan (2x-π) is π/2 radians or 90°

We know that tan (π/2) is undefined (a vertical asymptote)
so 2x - π = π/2
2x = 3π/2
x = 3π/4

So your function will have a vertical asymptote at
x = 3π/4 , and one every π/2 to the right or to the left after that

vertical asymptotes:
in radians : x = 3π/4 + kπ/2 , where k is an integer
in degrees : x = 135° + 90k° , where k is an integer

## Similar Questions

1. ### Trigonometry

Find the exact value of tan(a-b) sin a = 4/5, -3pi/2<a<-pi; tan b = -sqrt2, pi/2<b<pi identity used is: tan(a-b)=(tan a-tan b)/1+tan a tan b simplify answer using radicals. (a is alpha, b is beta)

3. ### Precalculus

Write an equation for rational function with given properties. a) a hole at x = 1 b) a vertical asymptote anywhere and a horizontal asymptote along the x-axis c) a hole at x = -2 and a vertical asymptote at x = 1 d) a vertical asymptote …
4. ### trigonometry

state the amplitude, period and phase shift of the function y=tan (20-80 degrees)
5. ### trigonometry

state the amplitude, period and phase shift of the function y = tan (2 theta- 180 degrees)
6. ### Trigonometry

What is the period of y = ã3sin (1/3x-ã1/3)?
7. ### Math-Trigonometry

Show that if A, B, and C are the angles of an acute triangle, then tan A + tan B + tan C = tan A tan B tan C. I tried drawing perpendiculars and stuff but it doesn't seem to work?
8. ### Math

f(x) = tan x / sin x Find the vertical asymptote. Describe its behavior to the left and right of the vertical asymptote.
9. ### math (trigonometry)

A=170 degree then prove that Tan A/2=-1-rot(1+Tan^2 A)/Tan A
10. ### Inverse trigonometry

Prove that- tan^-1(1/2tan 2A)+tan^-1(cotA)+tan^-1(cot^3A) ={0,ifpi/4<A<pi/2 {pi,0<A<pi/4 Where 2 small curly brackets are 1 big curly bracket

More Similar Questions