**Summary**

- Secant
*(sec)*is the reciprocal of cosine*(cos):*

- Cosecant
*(cosec)*is the reciprocal of*sin:*

- Cotangent
*(cot)*is the reciprocal of*tan:*

Recall, in case of a right angle triangle if we are given one length and one angle and we have to find a missing length or if we need to find a missing angle when two lengths are given we use SOH/CAH/TOA where:

SOH is shown in Fig 2

CAH is shown in Fig 3

TOA is applies to both Fig 2 & Fig 3

However, there are more trigonometric functions i.e

*Note: Remember that is not the inverse of and cannot be written as . This also applies to and .*

- Secant
*(sec)*is the reciprocal of cosine*(cos)* - Cosecant
*(cosec)*is the reciprocal of*sin* - Cotangent
*(cot)*is the reciprocal of*tan*

#### Graphical Comparison

#### Example 1

Q. In the triangle, find *cosec(A)*, *sec(A)*, and *cot(A)*.

*Solution:*

If we need to find out the angle A, we simply choose one of the above functions i.e

We know that:

Hence:

Where:

So:

°

##### Reference

- https://www.intmath.com/trigonometric-graphs/1-graphs-sine-cosine-amplitude.php
- https://www.intmath.com/trigonometric-graphs/4-graphs-tangent-cotangent-secant-cosecant.php
- http://www.nabla.hr/CL-GraphTransFun4.htm
- http://amsi.org.au/ESA_Senior_Years/SeniorTopic2/2d/2d_2content_6.html
- https://www.intmath.com/trigonometric-graphs/4-graphs-tangent-cotangent-secant-cosecant.php
- https://www.khanacademy.org/math/geometry-home/right-triangles-topic/reciprocal-trig-ratios-geo/a/reciprocal-trig-ratios