Evaluating inverse trig function

[cue928]

Homework Statement

We are being asked to evaluate the inverse trig function sin^-1 (1/ sqrt(2)).

Homework Equations

The Attempt at a Solution

I have no clue where to start. I have the unit circle, which makes sense to me if it was a trig function of a trig function, but when it's a trig function of a number not listed in a common unit circle diagram, I am thrown. Any guidance would be appreciated.

 

[Mark44]

Homework Statement

We are being asked to evaluate the inverse trig function sin^-1 (1/ sqrt(2)).

Homework Equations

The Attempt at a Solution

I have no clue where to start. I have the unit circle, which makes sense to me if it was a trig function of a trig function, but when it's a trig function of a number not listed in a common unit circle diagram, I am thrown. Any guidance would be appreciated.

x = sin^-1(1/sqrt(2)) <==> sin(x) = 1/sqrt(2)
Can you think of any angle in the first quadrant whose sine is 1/sqrt(2)?

 

[cue928]

x = sin^-1(1/sqrt(2)) <==> sin(x) = 1/sqrt(2)
Can you think of any angle in the first quadrant whose sine is 1/sqrt(2)?

The closest thing I saw was pi/4, but the sine there was root(2)/2. That's what the book shows but I don't see how they get that. I am really deficient in trig ;/

 

[eumyang]

They are the same. That's not a trig issue, it's an algebra issue.
$$\frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$$
Radical expressions aren't considered simplified if there is a radical in the denominator of a fraction. So one can rationalize the denominator (you can look it up).

 

[cue928]

Thank you.