3 Related hyperbolic functions
Given the trigonometric functions related functions can be defined; through the relations:
In an analogous way, given and we can introduce hyperbolic functions , and . These functions are defined in the following Key Point:
Key Point 6
Further Hyperbolic Functions
Task!
Show that
Use the identity :
Dividing both sides by gives
Exercises
-
Express
- in terms of and .
- in terms of and .
-
Express
- in terms of and .
- in terms of and , and then in terms of .
-
in terms of
and
.
3. Using only the and keys on your calculator (or key) find the values of
- ,
- ,
- .
-
-
- ,
- ,
- 0.3364,
- 0.2757
- 0.8436