If sec 48 = 1.4945, find csc 42

Because cos (x) = 1/sec (x), therefore

cos (48) = 1/1.4945 = 0.6691

The angle 48° is in quadrant 1, therefore cos, sin, tan, sec, csc and cot functions are all positive.

Note that sin (90° - x) = cos (x).

Therefore

sin (90 - 48) = cos (48)

sin (42°) = cos (48°) = 0.6691

Because csc (x) = 1/sin (x), therefore

csc (42°) = 1/sin (42°) = 1/0.6691 = 1.4945

Answer: 1.4945