This rule is fairly unique in the manner it calculates trig and hyperbolic functions.
(Flip to the back side of the rule; the tour starts there.)

Scale Function
P/Q/Q′ These scales compute the Pythagorean theorem $$c=\sqrt{a^2+b^2}$$. Q′ is an extension of Q.  Examples
$$\theta$$ Argument to trig functions in degrees. Read $$sin\,\theta$$ on P scale. Read $$tan\,\theta$$ on T scale on front side of rule. Read $$cos\,\theta$$ by setting left index of Q opposite $$sin\,\theta$$ on P scale and reading $$cos\,\theta$$ opposite right index of P. [This computes $$cos\,\theta=\sqrt{1-sin^2\theta}$$.]  Examples
$$R_\theta$$ Argument to trig functions in radians. Can be used with $$\theta$$ scale to convert between degrees and radians.
$$G_\theta$$ Argument to the Gudermannian (gd) function. Value of $$gd(x)$$ is read on the $$R_\theta$$ scale. Here's the magic to the Gudermannian function:
$$sinh\,x=tan(gd(x))$$
$$tanh\,x=sin(gd(x))$$
$$cosh\,x=sec(gd(x))$$
So by setting the cursor to $$x$$ on the $$G_\theta$$ scale, you read $$sinh\,x$$ on the T scale and $$tanh\,x$$ on the P scale. Read $$cosh\,x$$ by setting the left index of Q under the hairline and reading $$sech\,x$$ opposite the right index of P, flip the rule over and use C/CI to invert. If $$sinh\,x\le 1$$, there is another way to compute $$cosh\,x$$: set the value of $$sinh\,x$$ on Q under the hairline and read $$cosh\,x$$ on Q′. [The first method computes $$sech\,\theta=\sqrt{1-tanh^2\theta},$$ $$cosh\,x=1/sech\,x$$; the second computes $$cosh\,x=\sqrt{1+sinh^2x}$$.]  Examples

There are some links to documentation on this rule's main page.