The graph of a cosine function is periodic with period 2π and is similar to a graph of the sine function, with the difference that cosine function is shifted π/2 units left of the sine function for every corresponding value.
Period function of cosine and sine (red line) showing π/2 radian units shift:
To understand this π/2 radian units shift we equate five different degree measurements of cosine to sine:
Observe that in each value of corresponding cosine values equated to sine values that:
cos A° = sin (A + 90)°
or, in radian measure,
cos θ = sin (θ + π / 2)
… and it is this relationship that allows us to draw the cosine graph by shifting the sine graph by π/2 units to the left.
The π/2 shift of sine that equates the sine graph to the cosine graph can also be shown on a unit circle.
This unit circle shows the cos θ = sin α = sin (π − α) = sin (θ + π / 2):
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