Is -30 degree the same as 330 degree?

[Indranil]

Is -30 degree the same as 330 degrees? I am confused.

 

[MarkFL]

On the unit circle (standard position), -30° and 330° are coterminal, because their difference is an integral multiple of 360°.

 

[Dr.Peterson]

Is -30 degree the same as 330 degrees? I am confused.

For many purposes, the answer is yes: because the angles are coterminal, if all you care about is direction, you can call it either one.

Sometimes, you care about how far you have turned to get to a direction, and then you would consider them different.

What is the problem you are working on?

 

[Indranil]

For many purposes, the answer is yes: because the angles are coterminal, if all you care about is direction, you can call it either one.

Sometimes, you care about how far you have turned to get to a direction, and then you would consider them different.

What is the problem you are working on?

I am working on the directions of vectors.

 

[mmm4444bot]

I am working on the directions of vectors.

Measured from standard position, a vector at 330° is the same as a vector at -30°. They each point in the same direction because they're the same vector. It's the rotation that's different. Measured as 330°, the vector has rotated counter-clockwise, from standard position. Measured as -30°, the vector has rotated clockwise, from standard position.

Either way, the vector (i.e., terminal ray of angle) ends up in the same place. This is what is meant, when we say 330° and -30° are coterminal.

I encourage you to read some beginning lessons on trigonometry. It will help you understand basic vocabulary and definitions. Cheers :cool: