Lec 15 Fig 1: Unit circle and the graphs of sine and cosine

Consider a point $$A(x,y)$$ (the green point on the graph) on the unit circle. The function $f(\theta) = \sin(\theta)$ is defined as the $$y$$-coordinate of $$A$$ and $f(\theta) = \cos(\theta)$ is defined as the $$x$$-coordinate of $$A$$, where $$\theta$$ represents the angle measured from the $$+x$$-axis counterclockwise to the terminal arm (the line segment joining the centre to $$A$$). If we plot the graph of either $$f(\theta)$$ versus $$\theta$$ for $$\theta \in [0,2\pi]$$, we will get an oscillating curve (the blue curve) which starts from $$(0,0)$$ and ends at $$(2\pi,0)$$. This curve represent one cycle of $$\sin(\theta)$$ or $$\cos(\theta)$$. You may try to move the slider to change the value of $$\theta$$. The red line tells the value of $$f(\theta)$$.

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