TRIGONOMETRIC RATIOS OF SOME ANGLES

As trigonometry have different angles, for those different angles trigonometric ratios also have different values. In the trigonometry the angles 0°, 30°, 45°, 60°, 90°, 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, 360° are taken as standard angles.

We can find the trigonometric ratios of 0° and 90°. The following table shows the values of trigonometric ratios of the angles 0°, 30°, 45°, 60° and 90°.

Angles→↓	0°	30°	45°	60°	90°
sinθ	0	12	12√	3√2	1
cosθ	1	3√2	12√	12	0
tanθ	0	13√	1	3–√	∞
cosecθ	∞	2	2–√	23√	1
secθ	1	23√	2–√	2	∞
cotθ	∞	3–√	1	13√	0

PROCEDURES TO FIND THE TRIGONOMETRIC RATIOS

The standard angles i.e 0°, 30°, 45°, 60°, 90° is can be find out by simple way as given below: -

Process 1: -Put the number from 0 to 4 as  from 0 degree to 90 degree follows: -

0°	30°	45°	60°	90°
0	1	2	3	4

Process 2: -

Now divide each number by 4

0°	30°	45°	60°	90°
04	14	24	34	44

Process 3: -Take square root of all the numbers

0°	30°	45°	60°	90°
04−−√$\sqrt{\frac{\mathrm{<br>}}{\mathrm{}}}$	14−−√	24−−√	34−−√	44−−√

Process 4: -The values which are obtained at first are the values of sine of the standard angles.

Angles	0°	30°	45°	60°	90°
sin	0	12	12√	3√2	1

Process 5: -Then reversing the order, the value of cos of the standard angles are obtained.

Angles	0°	30°	45°	60°	90°
cos	1	3√2	12√	12	0

Process: -After dividing the value of sin by the value of cos, the values of tangent can be obtained: -

Angle	0°	30°	45°	60°	90°
tan	0	13√	1	3–√	∞  undefined

NOTE: - The reciprocal of sin, cos and tan are the values of cosec, sec and cot respectively.