find the reference and coterminal angle for 2456 and 740
if those are degrees, then just divide by 360 and use the remainder. If the remainder is not in QI, then just extract the reference angle as usual.
To find the reference angle for an angle, we need to subtract the nearest multiple of 360 degrees from the given angle.
For the angle 2456 degrees:
Step 1: Subtract the nearest multiple of 360 degrees from 2456 degrees.
2456 degrees - 6(360 degrees) = 2456 degrees - 2160 degrees = 296 degrees.
Therefore, the reference angle for 2456 degrees is 296 degrees.
To find the coterminal angle, we can add or subtract any multiple of 360 degrees to the given angle.
For the angle 2456 degrees:
Step 1: Add or subtract multiples of 360 degrees until we get another valid angle.
2456 degrees + 360 degrees = 2816 degrees.
2456 degrees - 360 degrees = 2096 degrees.
Therefore, the coterminal angles for 2456 degrees are 2816 degrees and 2096 degrees.
Next, let's find the reference and coterminal angle for 740 degrees:
For the angle 740 degrees:
Step 1: Subtract the nearest multiple of 360 degrees from 740 degrees.
740 degrees - 2(360 degrees) = 740 degrees - 720 degrees = 20 degrees.
Therefore, the reference angle for 740 degrees is 20 degrees.
To find the coterminal angle, we can add or subtract any multiple of 360 degrees to the given angle.
For the angle 740 degrees:
Step 1: Add or subtract multiples of 360 degrees until we get another valid angle.
740 degrees + 360 degrees = 1100 degrees.
740 degrees - 360 degrees = 380 degrees.
Therefore, the coterminal angles for 740 degrees are 1100 degrees and 380 degrees.
To find the reference and coterminal angle for a given angle, follow these steps:
1. Reference Angle: The reference angle is the smallest positive acute angle between the terminal side of the angle and the x-axis.
To find the reference angle for an angle:
- If the given angle is positive, subtract multiples of 360° until you get a value between 0° and 360°.
- If the given angle is negative, add multiples of 360° until you get a value between 0° and 360°.
So, for 2456°:
2456° - 6 * 360° = 56°
The reference angle for 2456° is 56°.
2. Coterminal Angle: Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of 360°.
To find the coterminal angle for an angle:
- To find a positive coterminal angle, add multiples of 360° to the given angle.
- To find a negative coterminal angle, subtract multiples of 360° from the given angle.
So, for 2456°:
2456° - 2 * 360° = 1736°
The positive coterminal angle for 2456° is 1736°.
Now moving on to 740°:
1. Reference Angle:
There is no need to adjust the given angle since it is already positive and between 0° and 360°.
Therefore, the reference angle for 740° is 740°.
2. Coterminal Angle:
To find a positive coterminal angle, add multiples of 360° to the given angle.
So, for 740°:
740° + 2 * 360° = 1460°
The positive coterminal angle for 740° is 1460°.