# I Can't Convert Sin(x) to Degrees

• Shoney45
In summary, the original firmware for the TI89 had an issue where arcsin would not work correctly. After following the instructions on the original post, everything worked fine.
Shoney45

## Homework Statement

I'm working through a Law of Sines problem. And along the way, I have discovered that sin(C) = .9796.s

I had thought from my trig days that I could find the angle whose sine is .9796 by finding the arcsin of.9796. But when I load this into my TI89, all it does is return the arcsin of .9796...except that .9796 is now in the form of a fraction.

So for the life of me, I can't figure out how to convert the sine of an angle into degree form.

You're probably in radians mode. Change the calculator mode to degrees and it should work.

Barring that, you can Google for the exact phrase (and without quotation marks):
arcsin 0.9796 in degrees

This triggers Google's built in calculator.

MATLABdude said:
You're probably in radians mode. Change the calculator mode to degrees and it should work.

Barring that, you can Google for the exact phrase (and without quotation marks):
arcsin 0.9796 in degrees

This triggers Google's built in calculator.

I've already toggled between degrees and radians, and it doesn't change anything. The problem is that I've got to get thsi figured out on a calculator because I've got to take the Praxis test and can't appeal to Google during the test.

This might be dumb, but did you try arcsin 0.9796? And turning off exact mode?

When all else fails, read the instructions.

SteamKing said:
When all else fails, read the instructions.

I did read the instructions. You'll notice that I input the value that = sin(x) such that sin^(-1)(x) should equal some value. And all my unit was outputting was sin(a big-arse fraction). So that was when I went to the internet for help.

When all else fails, read the original post first.

MATLABdude said:
This might be dumb, but did you try arcsin 0.9796? And turning off exact mode?

Golly, I'd sure try that if my unit was still failing me. But I reset the whole unit, and everything works fine now.

Glad to hear it worked. I can't tell if that was sarcastic or not, but this was an issue with the original firmware when I first bought mine a decade ago.

MATLABdude said:
Glad to hear it worked. I can't tell if that was sarcastic or not, but this was an issue with the original firmware when I first bought mine a decade ago.

No sarcasm towards you at all...only to the guy who himself was sarcastic. I love this site for the help I am able to get from nice you folks. You guys around here are really great.

## 1. Can you explain why we can't convert sin(x) to degrees?

The sine function is a mathematical function that takes an angle (in radians) as input and returns a ratio of the lengths of two sides of a right triangle. It does not have a unit of measurement, so it cannot be directly converted to degrees.

## 2. Is there a way to convert sin(x) to degrees?

No, there is no direct way to convert sin(x) to degrees. However, you can use the inverse sine function (arcsine) to find the angle in radians and then convert that angle to degrees.

## 3. Why do we use radians instead of degrees in trigonometry?

Radians are a more natural unit for measuring angles in mathematics because they are based on the properties of circles. One radian is equal to the angle at the center of a circle that subtends an arc equal in length to the radius of the circle. This makes calculations involving trigonometric functions, such as sine and cosine, simpler and more elegant.

## 4. Can you give an example of converting sin(x) to degrees using the inverse sine function?

Sure, let's say we have the value of sin(x) = 0.5. We can use the inverse sine function, sin^-1, to find the angle in radians: sin^-1(0.5) = 0.5236 radians. To convert this to degrees, we multiply by 180/pi (since there are 180 degrees in pi radians): 0.5236 * (180/pi) = 30 degrees.

## 5. Are there any special cases when converting sin(x) to degrees?

Yes, when using the inverse sine function, there are two possible values for the angle in radians that will give the same sin(x) value. This is known as the "principal value" and the other value is known as the "co-principal value". When converting to degrees, it is important to take into account which quadrant the angle is in to determine the correct principal value.

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