Download Sec, Cosec and Cot

Sec, Cosec and Cot
Secant, cosecant and cotangent, almost always written as sec, cosec and
cot are trigonometric functions like sin, cos and tan.
sec x =
1
cos x
cosec x =
1
sin x
1
= cos x
tan x
sin x
cot x =
Note, sec x is not the same as cos-1x (sometimes written as arccos x).
Remember, you cannot divide by zero and so these definitions are only valid when
the denominators are not zero.
Example
If sec x = 2, cos x = ½, x = 60º
Graphs of sec x and cosec x
Pythagorean Identities
The identity: sin²x + cos²x = 1 can be used to derive two more important
identities:
By dividing each of these terms by sin²x, we can derive a second identity:
•
1 + cot²x = cosec²x
By dividing (*) by cos²x, we arrive at the third (and final) identity:
•
tan²x + 1 = sec²x
These identities work for any angle x (measure in either degrees or
radians).