
The sine of $\angle P$ is the length of the side opposite $P$, $QR$, divided by the hypotenuse, $PR$: $$\sin{P} = \frac{QR}{PR}.$$The cosine of $\angle P$ is the length of the side adjacent to $P$, $PQ$, divided by the length of the hypotenuse, $PR$: $$\cos{P} = \frac{PQ}{PR}.$$The tangent of $\angle P$ is the length of the side opposite $P$, $QR$ divided by the side adjacent to $P$, $PQ$: $$\tan{P} = \frac{QR}{PQ}.$$
These ratios do not depend on the size of the triangle. If the triangle is scaled by a (positive) factor of $r$ then all three side lengths scale by $r$. The three trigonometric ratios are scaled by a factor of $\frac{r}{r} = 1$ and so they do not depend on the size of the triangle.

Exact values are entered in each row except for 15$^\circ$ and 75$^\circ$:
Angle (degrees) 
$\cos{x}$ 
$\sin{x}$ 
$\tan{x}$ 
$0$ 
1 
0 
0 
$15$ 
0.97 
0.26 
0.27 
$30$ 
$\frac{\sqrt{3}}{2}$ 
0.5 
$\frac{1}{\sqrt{3}}$ 
$45$ 
$\frac{\sqrt{2}}{2}$ 
$\frac{\sqrt{2}}{2}$ 
1 
$60$ 
0.5 
$\frac{\sqrt{3}}{2}$ 
$\sqrt{3}$ 
$75$ 
0.26 
0.97 
3.7 
$90$ 
0 
1 
 
Note that there is no entry for $\tan{90}$ because $\frac{1}{0}$ is not defined.
 We have $\tan{x} = \frac{\sin{x}}{\cos{x}}$ and this function is not defined when the denominator, $\cos{x}$, is zero. This happens, on the unit circle, for $x = 90$ and $x = 270$. For all other angles $0 \leq x \lt 360$, $\tan{x}$ has a well defined value.

There are a few patterns. First, the values of $\tan{x}$ for $0 \leq x \lt 90$ appear to be nonnegative and the value increases as $x$ increases. Further experimentation will show that this pattern continues. For example, $\tan{80} \approx 5.7$, $\tan{85} \approx 11$, and $\tan{89} \approx 57$. This makes sense since in a right triangle with an 89 degree angle and a 1 degree angle, the side opposite the 89 degree angle is much larger than the side adjacent and this disparity grows as the 89 angle grows closer and closer to 90 degrees.
Another pattern is perhaps harder to see. We can see that $\tan{60} = \frac{1}{\tan{30}}$ and, if we had exact values, we also have $\tan{75} = \frac{1}{\tan{15}}$. In general for a (nonzero) acute angle $x$, we have $\tan{x} = \frac{1}{\tan{(90x)}}$. This comes from the identities $\sin{x} = \cos{(90x)}$ and $\cos{x} = \sin{(90x)}$. To see why, note that
$$\begin{align} \tan{x} &= \frac{\sin{x}}{\cos{x}} \\ &= \frac{\cos{(90x)}}{\sin{(90x)}} \\ &= \frac{1}{\tan{(90x)}} \end{align}$$
 We can see that $\tan{0} = 0$ and we have also seen that for $0 \leq x < 90$, $\tan{x}$ grows as $x$ increases. There is no bound to how big $\tan{x}$ can be because when we write it as $\frac{\sin{x}}{\cos{x}}$ we can see that for acute angles just a little bit less than 90 degrees, the numerator of this fraction, $\sin{x}$, is close to 1 while the denominator, $\cos{x}$ is very close to zero. So the range of $\tan{x}$ for $0 \lt x \lt 90$ is all nonnegative real numbers.