Initial and terminal arm in trig

[supernova1203]

For some of the questions questions the initial arm is in the positive x and y quadrent and the terminal arm moves counter clockwise (+)this is considered positive , for some of them it is in the negative x and positive y quadrent, how does one determine where the initial arm is to be placed, and in which direction the terminal arm moves?

An example is

determine the reciprocal trigonometric ratios for 210 degrees.

I began by placing the initial arm in the positive x and positive y quadrent, and then moving the terminal arm counter clockwise till i reach 210 degrees in the 360 circle, which lands me on the 3rd quadrent, negative x and negative y quadrent. And the remaining angle is 60 degrees according to my calculations, but the book shows that the remaining angle is only 30 degrees, which means the terminal arm moved clockwise instead of counter clockwise.

I have included the diagram, how does one determine from which way does the angle travel? clockwise or counterclock wise?

 

[supernova1203]

i don't know why the attachment isn't working,
ah there we go finally!

 

[mharten1]

Always measure the angle in the counter clockwise direction. The angle that you have on there, in the clockwise direction, isn't 210 degrees. Measure it in the counter clockwise direction and it will be.

It doesn't matter what direction the terminal arm is moving. Just measure degrees counter clockwise.

I don't fully understand your question. This is the best I can do unless you can be a little bit clearer. Sorry!

 

[supernova1203]

Always measure the angle in the counter clockwise direction. The angle that you have on there, in the clockwise direction, isn't 210 degrees. Measure it in the counter clockwise direction and it will be.

It doesn't matter what direction the terminal arm is moving. Just measure degrees counter clockwise.

I don't fully understand your question. This is the best I can do unless you can be a little bit clearer. Sorry!

So.. basically that 30 degrees they obtained after the terminal arm went around 210 degrees counterclockwise.. was just relative to the closes axis? (which in this case was the x axis) and that's how the 30 degrees came about? So that resultant angle will always come depending on which axis is closer to the terminal arm?

 

[jhae2.718]

The 30 degrees in your image is called the reference angle, and is the angle between what you call the terminal arm and the x-axis.

Angles, by convention, are defined from the positive x-axis in the counter clockwise direction.

 

[mharten1]

So that resultant angle will always come depending on which axis is closer to the terminal arm?

As the above poster said, the 30 degree angle is called the reference angle. It doesn't come from the axis that's closest to the terminal arm. You determine the reference angle by using the X-Axis. Never the Y- Axis.

Perhaps this will help you understand better: Say that the angle of the terminal arm = θ.

If θ is in the 2nd quadrant, 180 - θ will give you the reference angle.

If θ is in the 3rd quadrant, θ - 180 will give you the reference angle.

Finally, if θ is in the 4th quadrant, 360 - θ will give you the reference angle.

It goes without saying that if θ is in the 1st quadrant, there will be no reference angle.

 

[jhae2.718]

Oops...mistyped that.

 

[supernova1203]

I love you guys, thanks for getting that stuff to make sense :) any idea where i can study about all the types of angles?

 

[mharten1]

I love you guys, thanks for getting that stuff to make sense :) any idea where i can study about all the types of angles?

What do you mean by "types of angles?"

Anyways, try this: http://www.regentsprep.org/Regents/math/algtrig/ATT3/referenceAngles.htm

 

[supernova1203]

What do you mean by "types of angles?"

Anyways, try this: http://www.regentsprep.org/Regents/math/algtrig/ATT3/referenceAngles.htm

Well I am sure there is some angle we get that is measured by the y-axis for example.

 

[eumyang]

Well I am sure there is some angle we get that is measured by the y-axis for example.

Maybe I'm misunderstanding you, but you may have missed what jhae2.718 said:

Angles, by convention, are defined from the positive x-axis in the counter clockwise direction.