what is the period trig?

Question

y=3 cos x/5

Answer 1

Function___Period
cos x_____2π
cos 2x____π
cos 4x____π/2
"
"
cos x/5___10π

Period of y = 3 cos x/5 is 10π

Answer 2

You should know that the period of y = cos(x) is 2 pi. The x is called the argument of the function. So y = sin(x) goes through a complete cycle of its values from 0 to 1 to 0 to -1 and back to 0 as x varies from 0 to 2pi. We say this mathematically by writing

y=sin(x) goes through one cycle of values as

0<= x <= 2pi

Now the argument in your function is x/5 so we need to find what values x must go through for x/5 to vary from 0 to 2pi.

That is, find x so 0<= x/5 <= 2pi which we solve by

multiplying by 5 to get 0 <= x <= 10pi so the period

of your function is 10pi - 0 = 10pi.

You would find the period of y =7 cos (pi/2 -pix) the same way.

You could memorize a formula to find the period but you will learn more and forget less if you reason it out as shown above.

Answer 3

10Pi