# What is 2nd sine?

Tags:
1. Jun 14, 2016

### Liam C

1. The problem statement, all variables and given/known data
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.
2. Relevant equations
sine = opposite/hypotenuse

3. 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?

#### Attached Files:

• ###### ok.png
File size:
3.5 KB
Views:
84
2. Jun 14, 2016

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.

3. Jun 14, 2016

### Staff: Mentor

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

4. Jun 14, 2016

### Staff: Mentor

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!).

5. Jun 14, 2016

### Staff: Mentor

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

6. Jun 14, 2016

### Liam C

Yes.

7. Jun 14, 2016

### Liam C

Also I tried using the inverse sine and it didn't give me the correct answer. It gives me 60.9

8. Jun 14, 2016

### Staff: Mentor

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

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

9. Jun 14, 2016

### Liam C

I don't know how to do that, unfortunately.

10. Jun 14, 2016

### Staff: Mentor

arcsine is the same as inverse sine.

11. Jun 14, 2016

### Staff: Mentor

12. Jun 14, 2016

### Liam C

13. Jun 14, 2016

### Staff: Mentor

Maybe double-check those numbers -- maybe there is a typo digit in there somewhere that is giving us the wrong answer...

14. Jun 14, 2016

### Liam C

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

15. Jun 14, 2016

### Staff: Mentor

arcsin(12.8/13.5) = 71.468. That looks to be the typo.

16. Jun 14, 2016

### Liam C

Ah, thanks so much! A silly textbook typo had me so confused!

17. Jun 14, 2016

### Staff: Mentor

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.

18. Jun 14, 2016

### Liam C

Yes, shift did it :)