What is the principle value of

Question

I really don't get this. Please provide explanation/step-by-step.

Answer 1

Usually, "principal values" of trig functions are defined as follows:

sin(x): values in [-π/2, π/2]

cos(x): values in [0, π]

tan(x) values in (-π/2, π/2)

So we can put tan^-1(17.8) in our calculator (with calculator in radian mode) and we get 1.515 since π/2 = 1.57, this value is in the range that fits the criteria above. So the principle value of tan^-1(17.8) = 1.515

And you can put sin^-1(-0.23) in our calculator (with calculator in radian mode) and we get -0.232 which also fits the criteria above so the principle value of sin^-1(-0.23) = -0.232