State the domain of fx tan x the range of fx sec x the dom

State the domain of f(x) = tan x; the range of f(x) = sec x; the domain of f(x) = tan^-1x; the range of f(x) = sin^-1 x; the range of f(x) = cos^- x; Find the exact value or approximate to 2 places. cos^-1(- squareroot/2) sin(arcsin 0.7) arctan(tan 11 pi/6) Write an algebraic expression for tan(arccos (x/5)). State the amplitude of: f(x) = - 4sin3x g(x) = (1/2) cos 7x Find the phase Shift of: f(x) = 5 + 2 sin (x - pi) g(x) = 4cos(x + 3 pi/2)

Solution

1. tanx

domain : all real numbers except pi/2 + k pi, k is an integer. because tanx is not defined at these values and hence these values should not be in the domain.

2. secx

domain : all real numbers except pi/2 + k pi, n is an integer.

3..arctanx

domain : (-pi/2 , pi/2)

4. arcsinx

domain : [-pi/2 , pi/2]

5.. arccosx

domain : [0 , pi ]