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
SOH is shown in Fig 2
CAH
CAH is shown in Fig 3
TOA
TOA is applies to both Fig 2 & Fig 3
More Tigonometric Functions
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