Give 2 positive and 2 negative angles that are coterminal with each angle?
1. 30 degrees
2. 135 degreed
3. -93 degrees
you can find coterminal angles by adding or subtracting multiples of 360 degrees to any given angle.
e.g. 30 + 360
so 30 and 390 are coterminal
135 + 720 = 755
so 135 and 755 are coterminal.
30 - 360 = -330
so 30 and -330 are ....etc.
1. positive 360 and 390
negative -330 and -360
2. positive 135 and 720
negative -330 and -390
either you misunderstood my examples or you are making arithmetic errors.
think of any angle.
To end up in the same position (coterminal) you would go around once, or twice, or three times...
either in a positive or in a negative direction, wouldn't you?
e.g. your angle of -93 degrees
adding 360 to it gives us 267
now adding another 360 gives us 627
subtraction 360 from -93 gives us -453
and subtracting another 360 yields -813
so -813, -453, 267 , and 627 are all coterminal with -93
taking the sine of each of those will yield the same answer
taking the cosine of each of those will yield the same answer
taking the tangent .....
To find angles that are coterminal with a given angle, we need to add or subtract multiples of 360 degrees (or 2π radians) to the original angle. This is because adding or subtracting a full revolution creates an angle that is in the same position.
Now, let's find two positive and two negative angles that are coterminal with each of the given angles:
1. For the angle of 30 degrees:
- Positive coterminal angle: Add 360 degrees to 30 degrees: 30 + 360 = 390 degrees.
- Negative coterminal angle: Subtract 360 degrees from 30 degrees: 30 - 360 = -330 degrees.
2. For the angle of 135 degrees:
- Positive coterminal angle: Add 360 degrees to 135 degrees: 135 + 360 = 495 degrees.
- Negative coterminal angle: Subtract 360 degrees from 135 degrees: 135 - 360 = -225 degrees.
3. For the angle of -93 degrees:
- Positive coterminal angle: Add 360 degrees to -93 degrees: -93 + 360 = 267 degrees.
- Negative coterminal angle: Subtract 360 degrees from -93 degrees: -93 - 360 = -453 degrees.
Therefore, the two positive coterminal angles with 30 degrees are 390 degrees and 495 degrees, while the two negative coterminal angles are -330 degrees and -225 degrees. Similarly, the two positive coterminal angles with 135 degrees are 495 degrees and 267 degrees, while the two negative coterminal angles are -225 degrees and -453 degrees.