Reference Angles: Find the Angle of $\frac{7\pi}{6}$

[1MileCrash]

Homework Statement

Find the reference angle of
- \frac{7\pi}{6}

Homework Equations

-

The Attempt at a Solution

I can tell you right now, that the answer is pi / 6.

My method would be to sketch the angle, find out at which point the appropriate x axis-coordinate will be used (for this example it would just be 180*, or Pi radians), and subtract from the original angle, considering only absolute value.

|(- 7 pi / 6) - (6 pi / 6) | = pi / 6

I understand what a reference angle is, but this is a step by step online problem that essentially requires me to go through *their* process, and I literally have no idea what they are doing. They seem to be making it leagues harder than what it actually is.

I am first instructed to sketch the angle in question and find what quadrant of a x-y graph the terminal side falls in.

Here is my sketch of the angle (this is actually the wrong sketch, I mixed up two problems, but regardless):

[PLAIN]http://img696.imageshack.us/img696/4065/graphsketch.png

Which shows that the angle terminates in quadrant I.

After entering that, I am told that "The angle corresponding to the branch of the X-axis that forms an acute angle with the terminal side of the given angle has the measure 0."

What? Clearly the sketch shows that the terminal side forms an angle of 0 with nothing. What are they talking about? Perhaps someone can rephrase this?

I can't figure out what they mean here, and it's hindering my progress. Why did I need to know the quadrant, exactly? What forms an angle with the measure 0? I see nothing of the sort here.

I understand exactly what a reference angle is, but I don't understand the method they are using to arrive at the answer.

 

[vela]

Homework Statement

Find the reference angle of
- \frac{7\pi}{6}

Homework Equations

-

The Attempt at a Solution

I can tell you right now, that the answer is pi / 6.

My method would be to sketch the angle, find out at which point the appropriate x axis-coordinate will be used (for this example it would just be 180*, or Pi radians), and subtract from the original angle, considering only absolute value.

|(- 7 pi / 6) - (6 pi / 6) | = pi / 6

I understand what a reference angle is, but this is a step by step online problem that essentially requires me to go through *their* process, and I literally have no idea what they are doing. They seem to be making it leagues harder than what it actually is.

I am first instructed to sketch the angle in question and find what quadrant of a x-y graph the terminal side falls in.

Here is my sketch of the angle (this is actually the wrong sketch, I mixed up two problems, but regardless):

[PLAIN]http://img696.imageshack.us/img696/4065/graphsketch.png

Which shows that the angle terminates in quadrant I.

Which angle are you referring to? The one in the original problem or the one in the wrong sketch? While the angle in the sketch clearly lies in quadrant I, the one in your original question lies in quadrant II.

After entering that, I am told that "The angle corresponding to the branch of the X-axis that forms an acute angle with the terminal side of the given angle has the measure 0."

What? Clearly the sketch shows that the terminal side forms an angle of 0 with nothing. What are they talking about? Perhaps someone can rephrase this?

I can't figure out what they mean here, and it's hindering my progress. Why did I need to know the quadrant, exactly? What forms an angle with the measure 0? I see nothing of the sort here.

I understand exactly what a reference angle is, but I don't understand the method they are using to arrive at the answer.

They're just saying the angle is measured relative to the +x-axis or -x axis depending on which quadrant the terminal side of the angle lies in. The phrase the branch of the X-axis that forms an acute angle with the terminal side of the given angle refers to the +x axis if the terminal side of the angle is in quadrant I or IV and to the -x axis if the terminal side of the angle is in quadrant II or III because that's how you get an acute angle rather than an obtuse angle. The sentence is simply saying that the angle that the +x or -x axis makes with itself is 0.