## Reciprocal Trigonometric Functions

The reciprocals of the three basic trig. functions, sine, cosine and tangent are of interest.

These are cosecant, secant and cotangent respectively. The three reciprocal trig. ratio are often abbreviated to cosec, sec and cot.

On calculators, the reciprocal trig. ratios are found by using the sin, cos and tan buttons followed by the reciprocal button.

e.g To find sec 30°, press      1.154700538 which can then be rounded off.

Note Do not use the cos-1 to find the secant!

### Graphs of Reciprocal Trig Functions

The graphs of the reciprocal trig. functions are quite unusual.

y = cosec x Features
The period is 2π
There are asymptotes are ± π , ± 2π , ...
The domain is R , the real numbers, x ≠ ± π , ± 2π ,...
The range is R , y ≤ -1 or y ≥ 1

y = sec x Features
The period is 2π
There are asymptotes are ± π / 2, ± 3π / 2, ...
The domain is R , the real numbers, x ≠ ± π / 2, ± 3π / 2...
The range is R , y ≤ -1 or y ≥ 1

y = cot x Features
The period is π
There are asymptotes are ± π, ± 2π, ...
The domain is R , the real numbers, x ≠ ± π, ± 2π...
The range is R , the real numbers.