Positive / negative angle help

[aisha]

Positive / negative angle help please

I just started the trig unit and was learning about positive and negative angles

The self exercise says find the corresponding positive angle of -75 degrees.

would the answer be 75 degrees? I know that -75 means the angle was made from the terminal arm turning clockwise.

How do u solve something like this?

 

[Hurkyl]

Are 75 and -75 the same angle?

(note: I'm guessing what your text means by "corresponding angle", but I think I'm probably right)

 

[aisha]

ok they are not the same angle looking at my protractor I am guessing that the answer might be 105? How do u set these kind of questions up?

 

[Hurkyl]

Those aren't the same angle either. After all, the difference between 75 degrees and 105 degrees is 30 degrees, and that's certainly not a zero angle...

 

[aisha]

ahhhhhhhhhhhhh HELP HELP HELP I don't know how to do this please help!

 

[Hurkyl]

Do you know any angles that are equal to the zero angle?

 

[Cyrus]

The anwser is 285 degrees. 360-75=285

 

[dextercioby]

Hello,Aisha.Don't dispare... :tongue2:
I believe it has to do with the trigonometric circlea nd the way the angles are pictured on it.For example,an angle of 40° is determined by the 0x axis and a line which goes through the center of the circle and which makes with th 0x axis the angle of 40°.Similar for every other angle between 0° (the 2 lines coincide,both being the 0x axis) and 360° which is in the same sitation with 0°,as a rotation of 360° brings every point in plane in the same place before the rotation.The sense of the positive angles is chosen as anticlockwise/trigonometric.Negative angles are considered in the clockwise direction,agia having the 0x axis as the frame of reference/as a fixed arm.
The problem is giving u an angle.It can be positive or negative.Let's assume it for simplicty to be positive,e.g.+45°.Then the corresponding negative angle is found from the equation:
'neg.angle=positive angle-360°=45°-360°=-335°'.
For a negative angle,the corresponding positive angle is given by:
'positive angle=negative angle+360°,which for an angle of -75°,it gives
-75°+360°=285°.

Daniel.

 

[Cyrus]

Hi dex,

I will put this on here too, its not quite as technical as your post, but I think its a little easier to follow .

Lets say your given an angle that is negative. That simply means that you start from the x-axis, and you rotate down, or clockwise to whatever angle is given. So for -75 degrees, you start at the x-axis, and you go down, or clockwise 75 degrees. And that is how you make a negative angle.

Now the question here asked for a positive angle that is equivalent to the negative angle. To do this, you can very easily see that you could also go the other way around to get to the same point. You could go counterclockwise, or rotate upwards, until you get to that point. In this case, if you rotate 285 counterclockwise, or upwards, you get to the same point as if you had rotated 75 degress clockwise, or down. Both are exactly the same. So in general, negative angles rotate down, or clockwise, and positive angles rotate up or counterclockwise. (unless they are defined with a different orientation.)

 

[aisha]

Thanks sooo much all of ur explanations are so well said that you've all made the beginning of this trig unit easier for me to understand thanks soooo much, I really appreciate it