Today we will study trigonometric ratios of 90°, 180°, and 270°.
Here angle AOP is of 90°.
According to the diagram, OP = r and the coordinates of point P are (0, r). So xcoordinate of point P is 0 and the ycoordinate of point P is r.
So, all the trigonometric ratios of O = 90° with
x = 0, y = r, r = r.
a) sin 90° = y/r
sin 90° = r/r
sin 90° = 1

b) cos 90° = x/r
cos 90° = 0/r
cos 90° = 0

c) tan 90° = y/x
tan 90° = r/0
tan 90° = ∞

d) csc 90° = r/y
csc 90° = r/r
csc 90° = 1

e) sec 90° = r/x
sec 90° = r/0 sec 90° = ∞

f) cot 90° = x/y
cot 90° = 0/r
cot 90° = 0
