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Use our reference angle calculator to find the reference angle for any angle in degrees or radians. Plus, learn the reference angle formulas.
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How to draw angle of 240o?
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How do you find the reference angle measuring X °?
Find the Reference Angle 240 degrees. 240° 240 °. Since the angle 180° 180 ° is in the third quadrant, subtract 180° 180 ° from 240° 240 °. 240°− 180° 240 ° - 180 °. Subtract 180 180 from 240 240. 60° 60 °. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with ...
How to Find a Reference Angle in Degrees. Finding a reference angle in degrees is straightforward if you follow the correct steps. 1. Identify your initial angle. For this example, we’ll use 440°. 2. The angle is larger than a full angle of 360°, so you need to subtract the total angle until it’s small. 440° - 360° = 80° . 3.
- Overview
- What is the reference angle?
- Finding the Reference Angle
- Finding the Reference Angle for Negative Angles and Angles Greater than 360° or 2𝛑
What is the reference angle?
The reference angle is the positive, acute angle that forms from a given angle’s terminal side and the x-axis. To find the reference angle, you simply determine what quadrant the given angle lies in on the coordinate plane. Then, you apply the reference angle formula based on the quadrant the angle is in. Read on below to learn what reference angles are, how to find them in degrees and radians, and what to do when the angle is negative or greater than 360° (or 2𝛑)!
The reference angle is made by the x-axis and terminal side of an angle.
Every angle has an initial side, which is the ray that falls on the x-axis, and a terminal side, which is the angle’s other ray.
The reference angle is the small angle formed by a given angle’s terminal side and the x-axis.
Reference angles are always positive and less than or equal to 90°.
Determine what quadrant the given angle is in.
The coordinate plane, or the intersection between the x-axis and y-axis, is split into 4 quadrants that span from 0° to 360° (or 0 to 2𝛑, if the angle is in radians). Look at the angle given to you and determine which quadrant it lies in based on its value.
Angles are between 0° to 90° or 0 to 𝛑/2.
Angles are between 90° to 180° or 𝛑/2 to 𝛑.
Angles are between 180° to 270° or 𝛑 to 3𝛑/2.
Angles are between 270° to 360° or 3𝛑/2 to 2𝛑.
Add or subtract 360° until the given angle is between 0° and 360°.
Sometimes, you have to find the reference angle for a given angle that’s less than 0 or greater than 360° (if it’s in radians, less than 0 or greater than 2𝛑). Finding the reference angle is still possible, you just first have to find its corresponding angle that’s between 0° and 360° (or between 0 and 2𝛑, if the angle is in radians).
If the angle is negative
, keep adding 360° until it is between 0° and 360°. If the angle is in radians, keep adding 2𝛑 until it is between 0 and 2𝛑.
If the angle is greater than 360°
, keep subtracting 360° until it is between 0° and 360°. If the angle is in radians, subtract 2𝛑 until it is between 0 and 2𝛑.
Jan 5, 2017 · Explained below. The angle of 240^o is drawn as shown in the figure. Angle of 0^o is taken to be along the positive x-axis. Then turn anti-clockwise by 240 degrees to draw the angle as desired. It is indicated along the line OP in the figure. The reference angle is the acute angle which this line OP makes with the x- axis.
The reference angle is the smallest possible angle made by the terminal side of the given angle with the x-axis. It is always an acute angle (except when it is exactly 90 degrees). A reference angle is always positive irrespective of which side of the axis it is falling.
The reference angle is the positive acute angle that can represent an angle of any measure. The reference angle $$ \text{ must be } < 90^{\circ} $$ . In radian measure , the reference angle $$\text{ must be } < \frac{\pi}{2} $$ .
