In standard position, an angle of 7pi/3 radians has the same terminal side as an angle of?
A)-420
B)120
C)60
D)625
pi/3 = 180/3 = 60
6 pi/3 = 360
so
7 pi/3 = 60
To find an angle with the same terminal side as an angle of 7π/3 radians, we have to subtract a full revolution (2π radians) from the given angle.
So, subtracting 2π radians from 7π/3 gives:
7π/3 - 2π = (21π - 6π)/3 = 15π/3 = 5π radians
Therefore, an angle of 7π/3 radians has the same terminal side as an angle of 5π radians.
However, none of the answer choices provided match 5π radians.
To determine the angle that has the same terminal side as an angle given in radians, you can use the concept of coterminal angles.
Coterminal angles are angles that have the same initial and terminal sides. To find coterminal angles, you can add or subtract integer multiples of 2π (or 360°) from the given angle.
In this case, we have an angle of 7π/3 radians. To find an angle with the same terminal side, we can add or subtract 2π from it.
Adding 2π to 7π/3 radians:
7π/3 + 2π = (21π + 6π) / 3 = 27π/3 = 9π radians
So, the angle of 7π/3 radians has the same terminal side as an angle of 9π radians.
Now, let's check the answer choices to see which one is equal to 9π radians:
A) -420: This is not a valid angle measure as angles are typically expressed in radians within the range of 0 ≤ θ < 2π.
B) 120: This is not equal to 9π radians.
C) 60: This is not equal to 9π radians.
D) 625: This is not equal to 9π radians.
None of the answer choices matches the coterminal angle of 9π radians. So, the answer is none of the above.