Thread: how does the coeffiecient of theta affect the number of periods?

1. how does the coeffiecient of theta affect the number of periods?

When solving an equation, does the coefficient create more solutions?

e.g.

tan x = 1 vs. tan 4x = 1

if the question asks for all solutions on [0, 2pi], will the latter equation have more solutions?

2. Re: how does the coeffiecient of theta affect the number of periods?

Hey OSUstudent223.

Hint: Think about many times the function will be repeated in the interval [0,2pi]. To know this get the period of the function and then calculate 2*pi/period to get the number of times the function repeats in that interval.

3. Re: how does the coeffiecient of theta affect the number of periods?

For a function y = a sin bx
A affects the amplitude i.e., max value of y and b affects the period
In this case the period would be 2pi/b.
Period is the smallest domain interval which corresponds to a complete cycle of the function.
Now you can work out for tan function
remember that for tan function amplitude is NONE because there is no maximum value and the period for tan function is pi