# Degrees and Radians [Solved!]

**phinah** 18 May 2018, 10:17

### My question

How is the sine of sixty degrees a negative number in radians?

### Relevant page

4. Integration: Basic Trigonometric Forms

### What I've done so far

When I enter sin 60 into my calculator in degrees the result returned is .866.

When I enter sin 60 in radians the result is -.3048.

X

How is the sine of sixty degrees a negative number in radians?

Relevant page
<a href="https://www.intmath.com/methods-integration/4-integration-trigonometric-forms.php">4. Integration: Basic Trigonometric Forms</a>
What I've done so far
When I enter sin 60 into my calculator in degrees the result returned is .866.
When I enter sin 60 in radians the result is -.3048.

## Re: Degrees and Radians

**Murray** 19 May 2018, 00:38

@Phinah

Using the conversion `pi` radians `= 180^@`, we have:

`1` radian `= (180^@)/pi`

`60` radians `= (60 xx 180^@)/pi`

Multiply this out and then convert it to an "ordinary" angle less than `360^"o"`

Can you see why `sin 60` radians is negative now?

X

@Phinah
Using the conversion `pi` radians `= 180^@`, we have:
`1` radian `= (180^@)/pi`
`60` radians `= (60 xx 180^@)/pi`
Multiply this out and then convert it to an "ordinary" angle less than `360^"o"`
Can you see why `sin 60` radians is negative now?

## Re: Degrees and Radians

**phinah** 26 May 2018, 13:47

NOW I CAN, thanks to you.

The answer is 3438`^@` rounded. Divided by 360`^@` shows that it is 9.55 complete revolutions which has a terminal side of around 198`^@`. Sine in the third quadrant is negative so this angle has a value of -.301.

Numbers have been rounded.

X

NOW I CAN, thanks to you.
The answer is 3438`^@` rounded. Divided by 360`^@` shows that it is 9.55 complete revolutions which has a terminal side of around 198`^@`. Sine in the third quadrant is negative so this angle has a value of -.301.
Numbers have been rounded.

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