The graphs of the sine and cosine functions are shown below.
graph of $y = \sin x$ 
graph of $y = \cos x$ 
The sine function gives the $y$values of points on the unit circle.
The cosine function gives the $x$values of points on the unit circle.
Since the unit circle has radius $\,1\,,$ all its points have coordinates between $\,1\,$ and $\,1\,.$
That's why both graphs (sine and cosine) are trapped between $\,y = 1\,$ and $\,y = 1\,.$
Here's a way you can visualize the graph of the sine function: Put your finger at the point $\,(1,0)\,$ on the unit circle. Twirl it around the circle counterclockwise (start UP). 
In Radian Measure, we ‘wrap’ the real number line around the unit circle.
In this way, every real number is associated with a point (called the terminal point) and a corresponding angle on the unit circle.
The real number is then the radian measure of this angle!
Wrap the real number line around the unit circle! Thus, every real number $\,x\,$ ... 
... is associated with a point on the unit circle ... 
... and a corresponding angle. 
As $\,x\,$ goes from $\,0\,$ to $\,\frac{\pi}{2}\,,$ $\,\sin x\,$ goes from $\,0\,$ to $\,1\,.$ (Remember: $\,\frac{\pi}{2}\,$ radians is $\,90^\circ\,$) 

As $\,x\,$ goes from $\,\frac{\pi}{2}\,$ to $\,\pi\,,$ $\,\sin x\,$ goes from $\,1\,$ back to $\,0\,.$ (Remember: $\,\pi\,$ radians is $\,180^\circ\,$) 

The entire discussion can be repeated to understand
the cosine—except that it gives the $x$values of the points, not the $y$values!
Here's how one of the graphics above would be adjusted to focus attention on the $x$value:
Properties of both sine and cosine:
sine has period $\,2\pi\,$: 
$\sin(x+2\pi) = \sin x\,$ for all real numbers $\,x\,$ More generally: $\sin(x+2\pi k) = \sin x\,$ for all integers $\,k\,$ and all real numbers $\,x\,$ 
cosine has period $\,2\pi\,$: 
$\cos(x+2\pi) = \cos x\,$ for all real numbers $\,x\,$ More generally: $\cos(x+2\pi k) = \cos x\,$ for all integers $\,k\,$ and all real numbers $\,x\,$ 
Take the sine curve and shift it $\,\frac{\pi}{2}\,$ units to the left—it turns into the cosine curve: $$ \cssId{s50}{\sin(x + \frac{\pi}{2}) = \cos x} $$ Take the cosine curve and shift it $\,\frac{\pi}{2}\,$ units to the right—it turns into the sine curve: $$ \cssId{s52}{\cos(x  \frac{\pi}{2}) = \sin x} $$


Thus, we have two new trigonometric identities!
For all real numbers $\,x\,$:
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
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