I was studying about trigonometric functions and I found that while defining trigonometric functions of any angle ( +ve or -ve and of any size), they take up two mutually perpendicular lines and a revolving line and then construct a perpendicular on the horizontal line from any point on revolving line. Then they define the base, the perpendicular and the revolving line segment. Then trigonometric ratios of the angle theta made by the revolving line are described as -
$\sin \theta =$ Perpendicular/Revolving segment
$\cos \theta =$ Base /Revolving segment
$\tan \theta =$ Perpendicular/Base
And subsequently their respective cofunctions .
For understanding , what actually a sine of acute angle is , we can think it of as a ratio of the opposite side to hypotenuse of an angle contained in a right triangle. But the problem arose when I had to visualize sine of an angle greater than $90^\circ$. This is because I cannot relate it as a ratio of sides of a triangle which makes it hard to grasp practically. I know some of the applications of trigonometric functions of angle greater than $90^\circ$ like while calculating work done , so there must be an intuitive description of such trigonometric functions but I couldn't reveal any.
Please help me understand, what trigonometric ratios of such angles mean practically. I don't prefer any theoretical explanations like that of Cartesian plane or input circle approach. Thanks in advance for that!