Question

how do i find the exact value for inverse functions? I do not understand how you know which quadrant it is or anything. Here are some examples:

a) Sin^-1 (0)
b) Sin^-1 (-1)
c) tan^-1 (0)
d) sin^-1 (square root 2/2)
e) tan^-1 (square root 3)
f) cos^-1 (- square root 3/3)

either pick one or all of them but step by step would be great thanks!

Answer 1

You can think of the other function if you like. It might make more sense:

a) Sin^-1 (0) ==> \(\sin(What) = 0\)
b) Sin^-1 (-1) ==> \(\sin(What) = -1\)
c) tan^-1 (0) ==> \(\tan(What) = 0\)
d) sin^-1 (square root 2/2) ==> \(\sin(What) = \sqrt{2}/2\)
e) tan^-1 (square root 3) f) ==> \(\tan(What) = \sqrt{3}\)
f) cos^-1 (- square root 3/3) ==> \(\cos(What) = 1/\sqrt{3}\)

Are you SURE that last one isn't supposed to be TANGENT?

Answer 2

I'll start.....

For sin^-1...your answer MUST be between -pi/2 and pi/2 inclusive. No exceptions.

So, in problem (a), sin ^-1 (0) = 0 (which is between -pi/2 and pi/s inclusive).

For part (b) sin^-1 (-1) = -pi/2 which is between -pi/2 and pi/2 inclusive.

For part (d), sin^-1 (sqrt(2)/2) = pi/4...which is between -pi/2 and pi/2 inclusive.

Just to make sure you understand what we are doing, in part (d), when we are finding sin^-1 (sqrt(2)/2)..what we want is to find the angle whose sine has a value of sqrt(2)/2..and that occurs at 45 degrees or pi/4.

Answer 3

tkhunny

yes i am sure the last one is not tangent.
I get that Sin(WHAT)=0
but both 0 and 180 deg. have 0 as sin. how do you know which one is the correct answer?

Answer 4

oh easyaspi
thank you! you answered my question!

Answer 5

0º and 180º are NOT both solutions.

The inverse sine function is defined ONLY on \(-90º \le What \le 90º\). This forces you to discard 180º.