The unit circle provides us with a visual understanding that the trigonometric functions of $\sin\theta$sinθ, $\cos\theta$cosθ and $\tan\theta$tanθ exist for angles larger than what can be contained in a rightangled triangle.
The unit circle definitions of $\sin\theta$sinθ and $\cos\theta$cosθ tell us that the value of these functions will be the $x$x and $y$yvalues respectively of a point on the unit circle after having rotated by an angle of measure $\theta$θ in the anticlockwise direction. Or, if $\theta$θ is negative, then the point is rotated in the clockwise direction.
Definition of $\cos\theta$cosθ and $\sin\theta$sinθ can extend beyond $0^\circ\le\theta\le90^\circ$0°≤θ≤90°. 
As we move through different values of $\theta$θ the value of $\cos\theta$cosθ and $\sin\theta$sinθ move accordingly between $1$−1 and $1$1.
The animation below shows this process for $y=\sin\theta$y=sinθ as $\theta$θ travels around the unit circle.

If we plot the values of $\sin\theta$sinθ and $\cos\theta$cosθaccording to different values of $\theta$θ on the unit circle, we get the following graphs:
$y=\sin\theta$y=sinθ 
$y=\cos\theta$y=cosθ 
The simplest way to calculate $\tan\theta$tanθ is to use the values in the above graphs to evaluate $\frac{\sin\theta}{\cos\theta}$sinθcosθ, which gives us the following graph:
$y=\tan\theta$y=tanθ 
Notice that all of these graphs are constructed with degrees on the horizontal axis. The function values behave in the same way as in the unit circle  for example, in the graph above of $y=\cos\theta$y=cosθ, we can see that it has negative $y$yvalues for all of the angles in the domain of $90^\circ<\theta<180^\circ$90°<θ<180°. These are the values associated with the second quadrant, that is, the "S" in ASTC, where we know that $\cos\theta$cosθ will be negative.
The graphs of $y=\cos\theta$y=cosθ and $y=\sin\theta$y=sinθ have certain common properties. Each graph demonstrates repetition. We call the graphs of $y=\cos\theta$y=cosθ and $y=\sin\theta$y=sinθ periodic, or cyclic. We define the period as the length of one cycle. For both graphs, the period is $360^\circ$360°.
An example of a cycle 
Because of the oscillating behaviour, both graphs have regions where the curve is increasing and decreasing. Remember that we say the graph of a particular curve is increasing if the $y$yvalues increase as the $x$xvalues increase. Similarly, we say the graph is decreasing if the $y$yvalues decrease as the $x$xvalues increase.
An example of where $y=\sin\theta$y=sinθ is decreasing 
In addition, the height of each graph stays between $y=1$y=−1 and $y=1$y=1 for all values of $\theta$θ, since each coordinate of a point on the unit circle can be at most $1$1 unit from the origin. This means, the range of both the $\sin\theta$sinθ and $\cos\theta$cosθ functions is between $1$−1 and $1$1.
$y=\tan\theta$y=tanθ is also periodic, however when you look closely at its graph you can see that its cycle length is only $180^\circ$180°. Its range is unbounded, and it also has values of $\theta$θ for which the function cannot be calculated. This means that, unlike $\sin\theta$sinθ and $\cos\theta$cosθ, it is not defined for all real values.
Consider the curve $y=\sin x$y=sinx drawn below and answer the following questions.
What is the $y$yintercept? Give your answer as coordinates in the form $\left(a,b\right)$(a,b).
What is the maximum $y$yvalue?
What is the minimum $y$yvalue?
Consider the curve $y=\cos x$y=cosx drawn below and determine whether the following statements are true or false.
The graph of $y=\cos x$y=cosx is cyclic.
True
False
True
False
As $x$x approaches infinity, the height of the graph approaches infinity.
True
False
True
False
The graph of $y=\cos x$y=cosx is increasing between $x=90^\circ$x=90° and $x=180^\circ$x=180°.
True
False
True
False
Given the unit circle, which of the following is true about the graph of $y=\tan x$y=tanx?
Select all that apply.
The graph of $y=\tan x$y=tanx repeats in regular intervals since the values of $\sin x$sinx and $\cos x$cosx repeat in regular intervals.
The graph of $y=\tan x$y=tanx is defined for any measure of $x$x.
Since the radius of the circle is one unit, the value of $y=\tan x$y=tanx lies in the region $1\le y\le1$−1≤y≤1.
The range of values of $y=\tan x$y=tanx is $\infty
The graph of $y=\tan x$y=tanx repeats in regular intervals since the values of $\sin x$sinx and $\cos x$cosx repeat in regular intervals.
The graph of $y=\tan x$y=tanx is defined for any measure of $x$x.
Since the radius of the circle is one unit, the value of $y=\tan x$y=tanx lies in the region $1\le y\le1$−1≤y≤1.
The range of values of $y=\tan x$y=tanx is $\infty
Understand the relationship between y = f(x) and y = f(x), where f(x) may be linear, quadratic or trigonometric.
Understand amplitude and periodicity and the relationship between graphs of related trigonometric functions, e.g. sin x and sin 2x.
Draw and use the graphs of y = asinbx + c, y = acos bx + c, y = atan bx + c where a is a positive integer, b is a simple fraction or integer (fractions will have a denominator of 2, 3, 4, 6 or 8 only), and c is an integer.