Question
Question: If \(\tanh x=\dfrac{12}{13}\), how do you find the values of the other hyperbolic functions at \(x\)...
If tanhx=1312, how do you find the values of the other hyperbolic functions at x ?
Solution
We explain the function arctan(x). We express the inverse function of tan in the form of arctan(x)=tan−1x. It’s given that tanx=1312. Thereafter we take all the other hyperbolic functions at x of that angle to find the solution. We also use the representation of a right-angle triangle with height and base ratio being 1312 and the angle being θ.
Complete step by step answer:
The hyperbolic functions are analogues of the ordinary trigonometric functions. All the usual relations are also used for the hyperbolic functions. It’s given that tanhx=1312. We can find the value of sechx from the relation of (sechx)2=1+(tanhx)2.
Putting the value, we get
(sechx)2=1+(1312)2 ⇒(sechx)2=169313
Now taking square root we get