On the left is a picture that shows the graph and the
period of sin(x). As you can see it takes the graph of sin(x) exactly 2Π to go a full cycle and return to y = 0. This is something that you should be familiar with already.
As you can see, the
period of this graph is 2Π. Nootice that the
formula for the period of sin(x) would also give you exactly 2Π .
By the formula, sin(1θ) has a period of (2Π)/1 = 2Π
On the left is a picture that shows the graph and the
period of sin(2θ). As you can see it takes the graph of sin(2θ) exactly Π to go a full cycle and return to y = 0. Therefore, the period of this graph is Π. Nootice that the
formula for the period of sin(x) would also give you exactly Π.
By the formula, sin(2θ) has a period of (2Π)/2 = Π
Below is a picture that shows the graph and the
period of sin(½θ). As you can see it takes the graph of sin(½θ) 4Π to go a full cycle and return to y = 0. Therefore, the
period of this graph is 4 Π. The
formula for the period of sin(½θ) would also give you 4 Π.
By ourformula, sin(4θ) has a period of (2Π)/½ = 4Π