## Blog-77

Today we will study trigonometric ratios of 90°, 180°, and 270°.

5) Trigonometric ratios of an angle O = 90°
Here angle AOP is of 90°.
According to the diagram, OP = r and the coordinates of point P are (0, r). So x-coordinate of point P is 0 and the y-coordinate 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

6) Trigonometric ratios of an angle O = 180°
Here angle AOP is of 180°.
According to the diagram, OP = r and the coordinates of point P are (-r, 0). So x-coordinate of point P is -r and the y-coordinate of point P is 0.

So, all the trigonometric ratios of O = 180° with
x = -r, y = 0, r = r.

 a) sin 180° = y/r     sin 180°  = 0/r        sin 180°  = 0 b) cos 180° = x/r      cos 180° = -r/r      cos 180° = -1 c) tan 180° = y/x      tan 180° = 0/-r        tan 180° = 0 d) csc 180° = r/y     csc 180° =  r/0     csc 180° =  ∞ e) sec 180° = r/x     sec 180° = r/-r              sec 180° = -1 f) cot 180° = x/y     cot 180° = -r/0      cot 180° = -∞

7) Trigonometric ratios of an angle O = 270°
Here angle AOP is of 270°.
According to the diagram, OP = r and the coordinates of point P are (0, -r). So x-coordinate of point P is 0 and the y-coordinate of point P is -r.

So, all the trigonometric ratios of O = 270° with
x = 0, y = -r, r = r.

 a) sin 270° = y/r     sin 270° = -r/r        sin 270° = -1 b) cos 270° = x/r      cos 270° = 0/r      cos 270° = 0 c) tan 270° = y/x     tan 270° = -r/0       tan 270° = ∞ d) csc 270° = r/y     csc 270° =  r/-r     csc 270° =  -1 e) sec 270° = r/x     sec 270° = r/0     sec 270° = ∞ f) cot 270° = x/y    cot 270° = 0/-r       cot 270° = 0

Actually, it is very easy to understand the concept once we found out the values of x, y and r for the point P on the terminal ray.

In the next Blog, we will study all the trigonometric ratios for the following groups.
Group-01: 120° (90° + 30°), 210° (180° + 30°), 300° (270° + 30°).
Group-02: 135° (90° + 45°), 225° (180° + 45°), 315° (270° + 45°).
Group-03: 150° (90° + 60°), 240° (180° + 60°), 330° (270° + 60°).

Anil Satpute