How do you solve cscG= 2.3456?

1 Answer
Alan P.
Oct 7, 2015

Within the range [0,2pi)
G=0.440432 " (radians)" or pi-0.440432 " (radians)"

Explanation:

csc(G) = 2.3456

rarrcolor(white)("XXX")sin(G)=1/2.3456

arcsin(sin(G)) = G if we restrict G to (-pi/2,pi/2]

arcsin(1/2.3456) = 0.440432 (using a calculator)

Within the full [0,2pi] range an alternate possibility exists in Q II for which the sin has the same value; namely
color(white)("XXX")pi - 0.440432

Note: if you need to remove the [0,2pi] limitation allow (+2npi, AAn in ZZ) for both possible solutions

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