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### 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.

@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°

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°

Can you see why sin 60 radians is negative now?

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.