Period of a function?

Question

Which of the following is the period of f(x) = 2cos(4x + pi) -1 ?

i dont know how to find the period?

especially with the trig function

Answer 1

The period of sin(x) and cos(x) are 2pi, but if you multiply x in those functions, the function will need less change in x go through the period.  The period of cos(2x) will move through two periods in the space that cos(x) moves through one.  Thus it's period is half that, or just pi.

Multiplying the function by a value will not change the period.  It'll only make the crests and troughs more extreme.  Adding anything to x will only move the function to the right or left.  The period stays the same.  Adding or subtracting to the function will only move the graph up or down, again not affecting the period.

So the only thing that's affecting that 2pi default is the 4x.  You should be able to figure it from here.

Answer 2

Y = A (Bx + C ) + D



to find period you do 2pi/B       2pi/4    (B is 4)

the Answer is pi/2

for tan and cot you do pi/B