# What is 2nd sine?

## Homework Statement

A triangle with a hypotenuse of 13.5 and height of 11.8. Find the measure of angle P.
Angle p is on the same line as the 90 degree angle and I found out that it must be sine.

## Homework Equations

sine = opposite/hypotenuse

## The Attempt at a Solution

sin p = 11.8/13.5
sin p = .874

Textbooks answer: sin p = 71.468
It says I need to use something called 2nd sine like this: 2nd sin(11.8/13.5), which I can't find on my calculator and hasn't been introduced in the textbook until now. It doesn't explain 2nd sin. What does it mean and how do I go about solving this on my own?

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Homework Helper
Gold Member
It would appear "2nd" is supposed to be an inverse function: You're finding the angle whose sine is 11.8/13.5. That is often written as ## \sin^{-1}(11.8/13.5) ##. The "2nd" is apparently referring to a "second" (inverse) function.

berkeman
Mentor
Textbooks answer: sin p = 71.468
That looks more like the angle p. Try looking for arcsin on your calculator to go from the sine value to the angle...

EDIT -- Beaten to the punch by Charles berkeman
Mentor
Textbooks answer: sin p = 71.468
BTW, I get a slightly different answer for the angle. I'll check the rest of your work (unless Charles beats me to that too!).

berkeman
Mentor
Angle p is on the same line as the 90 degree angle and I found out that it must be sine.
Are you sure you have the angle p shown in the right place?

Are you sure you have the angle p shown in the right place?
Yes.

Are you sure you have the angle p shown in the right place?
Also I tried using the inverse sine and it didn't give me the correct answer. It gives me 60.9

berkeman
Mentor
Yes.
So what do you get for arcsin(11.8/13.5 )

EDIT -- Right, that's what I got.

So what do you get for arcsin(11.8/13.5 )

EDIT -- Right, that's what I got.
I don't know how to do that, unfortunately.

berkeman
Mentor
I don't know how to do that, unfortunately.
arcsine is the same as inverse sine.

berkeman
Mentor
• Liam C
berkeman
Mentor
hypotenuse of 13.5 and height of 11.8.
Maybe double-check those numbers -- maybe there is a typo digit in there somewhere that is giving us the wrong answer...

Maybe double-check those numbers -- maybe there is a typo digit in there somewhere that is giving us the wrong answer...
Unfortunately no :(
I am starting to think there might be a typo in the text book given the fact what it's telling me to do gives me a completely wrong answer

berkeman
Mentor

## The Attempt at a Solution

sin p = 11.8/13.5
sin p = .874

Textbooks answer: sin p = 71.468
arcsin(12.8/13.5) = 71.468. That looks to be the typo. • Liam C
arcsin(12.8/13.5) = 71.468. That looks to be the typo. Ah, thanks so much! A silly textbook typo had me so confused! Mark44
Mentor
It says I need to use something called 2nd sine like this: 2nd sin(11.8/13.5),
Some calculators have a button labeled "2nd". When you press it, the calculator uses the function behind (or above) a given button.

On my calculator, a CASIO model, there is a button labeled SHIFT, in orange letters. Just above my button labeled "sin" is label, in orange letters, for the inverse function "sin-1". There are inverse functions for sine, cosine, and tangent, as well as log, ln (natural log) and a few others. All of the inverse functions are accessed by pressing the SHIFT button. On yours I'd be willing to bet there's a "2nd" button.

• Liam C and berkeman
Some calculators have a button labeled "2nd". When you press it, the calculator uses the function behind (or above) a given button.

On my calculator, a CASIO model, there is a button labeled SHIFT, in orange letters. Just above my button labeled "sin" is label, in orange letters, for the inverse function "sin-1". There are inverse functions for sine, cosine, and tangent, as well as log, ln (natural log) and a few others. All of the inverse functions are accessed by pressing the SHIFT button. On yours I'd be willing to bet there's a "2nd" button.
Yes, shift did it :)