find the largest negative co terminal angle of -417 degrees.
To find the largest negative coterminal angle of -417 degrees, we need to find an angle that, when added to -417 degrees, results in an angle within the same angle measure range.
In this case, the angle measure range is 360 degrees, as an angle completes a full revolution in that range.
Step 1: Determine the coterminal angles
To find the coterminal angles, add or subtract multiples of 360 degrees.
a) Adding 360 degrees to -417 degrees:
-417 + 360 = -57
b) Subtracting 360 degrees from -417 degrees:
-417 - 360 = -777
Step 2: Identify the largest negative coterminal angle
Since we're looking for the largest negative coterminal angle, we need to go backwards, which means subtracting multiples of 360 degrees.
The largest negative coterminal angle would be -777 degrees, as it is the furthest in the negative direction within the range of a negative coterminal angle.
Therefore, the largest negative coterminal angle of -417 degrees is -777 degrees.