Why do we need values greater than 90 degrees?

[Frigus]

I can't understand how can we assign values greater than 90 to trigonometric functions as right angle triangle can't exist if one angle is more than 90 degree. For example if I say sin 30 according to me it means that ratio of perpendicular and hypotenuse is 1/2 at 30 degree but how can we say something like this in angles greater than 120.

 

[fresh_42]

This is because we do not consider only (right) triangles, but the full circle instead which we divide into degrees. E.g. look at a compass and how pilots and captains measure their direction. And even in triangles, there are triangles with angles greater than 90° or 120°, and we also consider the outer angles, the complementary angles to the inner ones.

 

[PeroK]

I can't understand how can we assign values greater than 90 to trigonometric functions as right angle triangle can't exist if one angle is more than 90 degree. For example if I say sin 30 according to me it means that ratio of perpendicular and hypotenuse is 1/2 at 30 degree but how can we say something like this in angles greater than 120.

It's called a generalisation. Imagine the unit circle and start with your right-angle triangle in the first quadrant. You notice that:

$x = \cos \theta \$ and $y = \sin \theta$

As you continue round the circle, you could extend your definition of sine and cosine by taking these equations to define $\sin \theta$ and $\cos \theta$.

And then you have something even more useful than restricting yourself to angles less than $\pi/2$.

 

[WWGD]

You can even define a full coordinate system, polar coordinates, using sin, cos.

 

[HallsofIvy]

IF you are only using the "trig functions" on right triangles then there is no reason to use angles greater than 90 degrees. But generalizations of the trig functions (sometimes renamed "circular functions") are very useful as "periodic functions" modeling repetitive phenomena. As functions, we want them defined for all real numbers.

 

[Stephen Tashi]

I can't understand how can we assign values greater than 90 to trigonometric functions as right angle triangle can't exist if one angle is more than 90 degree.

Have you studied trigonometry as it is defined using the unit circle? If so, you understand how it is done. Perhaps your question is why it is done. Do you want to know why defining the trigonometric functions for all angles is useful?