Question

How do you solve the equation `cottheta=12.3` for `0<theta<2pi`?

Answer 1

`theta ~~ 0.8112 or 3.2227` (radians) `[= 4.648^@ or 184.648^@]`

Explanation:

In theory if `cos(theta)=12.3` then, for `thetain[0,pi),`theta=arccot(12.3)#

...but my calculator will only give me `arctan` values,
so
`color(white)("XXX")`since `tan(theta)=1/cot(theta)`

For `theta in [0,pi)`, I used my calculator to evaluate
`color(white)("XXX")arctan(1/12.3)~~0.81122392` (radians)

For `theta in [0,color(black)(2pi))`, it is necessary to include the angle in Q III by adding `pi` to this to obtain an additional angle with this measurement.