Question

How do you find the exact value of the 6 trig functions for x=740?

Answer 1

Assuming that you mean `740^@`, I'm fairly sure that the exact value cannot be written using algebraic combinations of roots of real numbers.

`sin 740^@ = sin 20^@`, but using Galois Theory it can be shown that this cannot be expressed using algebraic combinations of roots of real numbers.

(It is the reason trisecting an angle with compass and straightedge is impossible.)

Answer 2

Calculator gives:
`sin(740°) = sin (720° + 20°) = sin(20°) = 0.34`
`cos^2(20°) = 1 - sin^2(20°) = 0.884 rArr cos(20°) = 0.94`
`tan(20°) = 0.34/0.94 = 0.36`
`cot(20°) = 1/0.36 = 2.78`
`sec(120°) = 1/0.94 = 1.06`
`csc(120°) = 1/0.34 = 2.94`