Find the coterminal angles: one positive one negative angle. 55° and (9(3.14)/5) answer degrees in radians and radians in degrees
55° + 360k are all coterminal for any integer k.
9/5 π + 2kπ are all coterminal for any integer k.
So, pick a positive and negative k
To find the coterminal angles, we need to add or subtract multiples of 360° or 2π radians.
For the angle 55°:
To find a positive coterminal angle, we add multiples of 360°.
55° + 360° = 415°
To find a negative coterminal angle, we subtract multiples of 360°.
55° - 360° = -305°
For the angle (9(3.14)/5) radians:
To find a positive coterminal angle, we add multiples of 2π radians.
(9(3.14)/5) + 2π = (9(3.14)/5) + (2 * 3.14) = (9(3.14)/5) + 6.28 ≈ 9.0044 radians
To find a negative coterminal angle, we subtract multiples of 2π radians.
(9(3.14)/5) - 2π = (9(3.14)/5) - (2 * 3.14) = (9(3.14)/5) - 6.28 ≈ -3.1416 radians
Converting the angles to degrees:
415° in radians is approximately (415 / 180) * π ≈ 7.2309 radians
-305° in radians is approximately (-305 / 180) * π ≈ -5.3379 radians
9.0044 radians in degrees is approximately (9.0044 / π) * 180 ≈ 515.34°
-3.1416 radians in degrees is approximately (-3.1416 / π) * 180 ≈ -179.99°
To find the coterminal angles, we need to add or subtract multiples of 360 degrees (or 2π radians) to the given angle.
1. Positive Coterminal Angle (in degrees):
To find the positive coterminal angle, add 360 degrees to the given angle until you get a positive value less than 360 degrees.
For 55 degrees:
55 + 360 = 415 degrees
So, the positive coterminal angle for 55 degrees is 415 degrees.
2. Negative Coterminal Angle (in degrees):
To find the negative coterminal angle, subtract 360 degrees from the given angle until you get a negative value greater than -360 degrees.
For 55 degrees:
55 - 360 = -305 degrees
So, the negative coterminal angle for 55 degrees is -305 degrees.
Now, let's convert the angles to radians.
3. Convert an Angle to Radians:
To convert an angle in degrees to radians, you can use the formula: radians = degrees * (π/180).
For the positive coterminal angle:
radians = 415 * (π/180) ≈ 7.225 radians
For the negative coterminal angle:
radians = -305 * (π/180) ≈ -5.327 radians
Now, let's convert the coterminal angles back to degrees.
4. Convert Radians to Degrees:
To convert an angle in radians to degrees, you can use the formula: degrees = radians * (180/π).
For the positive coterminal angle:
degrees = 7.225 * (180/π) ≈ 414.86 degrees
For the negative coterminal angle:
degrees = -5.327 * (180/π) ≈ -305.11 degrees
So, the coterminal angles for 55 degrees are 415 degrees (positive) and -305 degrees (negative) in degrees, and approximately 7.225 radians (positive) and -5.327 radians (negative) in radians.