Refrence Angles & Positive/Negative Angles(Coterminals) HOW?

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In summary, to find one positive and one negative angle that are coterminal with a given angle, add or subtract 2\pi until you get a positive or negative angle respectively. For finding the reference angle of an angle, continue adding or subtracting 2\pi until you get a value between 0 and 2\pi, depending on the quadrant the angle is in.
  • #1
mathzeroh
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my question is, how do you "Find one positive angle and one negative angle that are coterminal with each angle." :

For example:

[tex]\frac{5\pi}{12} [/tex]


And also, I had a question on this as well:

Find the reference angle for each angle with the given measure.
[tex]\frac{12\pi}{5} [/tex]

i noe that you have to see what quadrant it is in, then from there, you use the Reference Angle Rule, whichever one. But what if the measure is a negative number? Like for example, [tex]-210\circ[/tex]?? What would you do here?

if anyone can help me with these i'd be really gratefull! thanks!
 
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  • #2
mathzeroh said:
my question is, how do you "Find one positive angle and one negative angle that are coterminal with each angle."
Given some angle, x, you can find a positive angle co-terminal with x by adding [itex]2\pi[/itex] to x until you get a positive number, and you can figure out how to find a negative angle.
Find the reference angle for each angle with the given measure.
[tex]\frac{12\pi}{5} [/tex]
To find the reference angle for any angle, keep continuing to add or subtract [itex]2\pi[/itex] until you get a value, x, such that [itex]0 \leq x < 2\pi[/itex]. Of course, you'll have to figure out whether you need to add, subtract, or neither.
 
  • #3


To find a positive and negative coterminal angle with a given angle, you can add or subtract 2π (or 360°) from the given angle. This is because 2π (or 360°) is the period of a circle, meaning that adding or subtracting it will bring you back to the same angle.

For example, if the given angle is \frac{5\pi}{12}, you can add 2π to get a positive coterminal angle: \frac{5\pi}{12} + 2\pi = \frac{29\pi}{12}. You can also subtract 2π to get a negative coterminal angle: \frac{5\pi}{12} - 2\pi = -\frac{19\pi}{12}.

For the angle \frac{12\pi}{5}, you can use the same method. Adding 2π gives a positive coterminal angle: \frac{12\pi}{5} + 2\pi = \frac{22\pi}{5}. Subtracting 2π gives a negative coterminal angle: \frac{12\pi}{5} - 2\pi = -\frac{8\pi}{5}.

When finding the reference angle for a given angle, you need to consider the quadrant in which the angle lies. For positive angles, the reference angle will always be the angle formed between the terminal side of the given angle and the x-axis. For negative angles, the reference angle will be the angle formed between the terminal side of the given angle and the negative x-axis.

For the angle -210°, you can first convert it to radians by multiplying by \frac{\pi}{180}. This gives -\frac{7\pi}{6}. Since this angle falls in the third quadrant, the reference angle will be the angle formed between the terminal side and the negative x-axis, which is \frac{\pi}{6}.

I hope this helps with your understanding of reference angles and coterminal angles. Remember to always consider the quadrant and use the period of 2π (or 360°) when finding coterminal angles.
 

What are reference angles?

Reference angles are angles that are used as a reference point to find the exact value of an angle. They are always measured from the x-axis and fall in the range of 0 to 90 degrees.

How do you find the reference angle of an angle?

To find the reference angle of an angle, you can use the following steps:1. Determine the quadrant in which the angle falls.2. If the angle is in the first or fourth quadrant, the reference angle is the same as the original angle.3. If the angle is in the second or third quadrant, subtract the angle from 180 degrees to find the reference angle.

What are positive and negative angles?

Positive angles are measured counterclockwise from the x-axis, while negative angles are measured clockwise from the x-axis. Positive angles are considered to be in the standard position, while negative angles are considered to be in the negative position.

What are coterminal angles?

Coterminal angles are angles that have the same initial and terminal sides, but differ in the number of rotations or revolutions. In other words, they have the same reference angle but may differ in their measurements.

How do you find coterminal angles?

To find coterminal angles, you can add or subtract 360 degrees to the original angle. This will result in an angle that has the same reference angle but a different measurement. For example, if the original angle is 45 degrees, then adding 360 degrees will result in a coterminal angle of 405 degrees.

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