Which of the following is coterminal with ?
A)-237
B)33
C)-33
D)597
coterminal with 237degrees*
To determine which of the given options is coterminal with an angle, we need to find other angles that have the same initial and terminal sides as the given angle.
The given angle is not provided, so let's assume the missing angle is 33 degrees.
To find coterminal angles, we can add or subtract multiples of 360 degrees (or 2π radians).
a) -237 degrees:
We can subtract 360 from 33 degrees multiple times until we get a negative angle:
33 - 360 = -327 (not coterminal yet)
-327 - 360 = -687 (not coterminal yet)
-687 - 360 = -1047 (not coterminal yet)
-1047 - 360 = -1407 (not coterminal yet)
...
Therefore, -237 degrees is not coterminal with 33 degrees (missing angle).
b) 33 degrees:
Given that we assume the missing angle is 33 degrees, it is indeed coterminal with itself. So, 33 degrees is coterminal with 33 degrees (option B).
c) -33 degrees:
We can subtract 360 from 33 degrees:
33 - 360 = -327 (not coterminal yet)
However, -33 degrees can be obtained by subtracting another 360 degree:
-327 - 360 = -687
Therefore, -33 degrees is coterminal with 33 degrees (option C).
d) 597 degrees:
We can subtract 360 from 33 degrees multiple times until we find a positive angle:
33 + 360 = 393 (not coterminal yet)
393 + 360 = 753 (not coterminal yet)
Therefore, 597 degrees is not coterminal with 33 degrees (missing angle).
Summarizing our findings:
- Option A (-237 degrees) is not coterminal with 33 degrees.
- Option B (33 degrees) is coterminal with 33 degrees.
- Option C (-33 degrees) is coterminal with 33 degrees.
- Option D (597 degrees) is not coterminal with 33 degrees.
Hence, the correct answer is option C.