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Period of sine and cosine graphs and their equations

Connection between period of graph, equation and unit Circle

The period of sine and cosine equations relates to how often the graph goes a full repition around the unit circle. The period is how long it takes for sine or cosine to return to the same place.

Formula for period of sin(x) & cos(x)


formula for period of sine and cosine
picture of period of sinx 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
diagram of period of graph of sin2x 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
picture of graph and period of sin of half x

Demonstration of Period of sine Graph & Connection Unit Circle

Open this demonstration in its own window(opens up new window, making it easier to see entirety of demonstration)