This question might be basic, but it is confusing me:
$$\begin{align} \text{sine of $\theta$} &= \frac{\text{length of opposite}}{\text{length of hypotenuse}} \\[4pt] \text{cosine of $\theta$} &= \frac{\text{length of adjacent}}{\text{length of hypotenuse}} \\[4pt] \text{tangent of $\theta$} &= \frac{\text{length of opposite}}{\text{length of adjacent}} \end{align}$$
Thus, trigonometric ratios are just ratios of lengths of sides of a right-angled triangle.
So how come their sign changes in different quadrants? Lengths don't have signs.
Eg. $\sin 45^\circ = 0.7071\dots$, whereas $\sin(-45^\circ) = -0.7071\dots$. Why ?