# Understanding the values of trigonometric functions for angles not between $0^\circ$ and $90^\circ$

We know that values of $$\sin 400^{\circ} , \cos 135^{\circ} , \cos 0^{\circ}$$ are $$0.64, -0.71, 1$$ respectively. But I think these values doesn't make any sense at all. Because we can't have any triangle with an angle of $$400^{\circ}$$ and we also can't have any sort of triangle with one angle being $$0^{\circ}$$ (or can we?). I am very confused with it. How can we find value of any trigonometric ratio for angles not in between $$0^{\circ}$$ & $$90^{\circ}$$ , if we can't make any triangle with these angles even in fantasy. So what are these $$0.64, -0.71, 1"?$$

We can think about trigonometric functions as those whose inputs are angles and outputs are scalars. For instance $$sin(\theta)=x$$. $$\theta$$ is the angle between your point of interest and 0 on the unit circle.
For the sine function the output scalar is the vertical component for the point on the unit circle which is an angle $$\theta$$ from 0. Alternatively cosine is the horizontal component.