Answer: B = B ∈ {70° + n*360° I n ∈ Z } where Z is the set of the integer numbers.
Step-by-step explanation:
If we have an angle A, the other angles that have the same terminal arm than A can be written as:
B = A + n*360°
Here B is a "coterminal" angle to A. (they have the same terminal side)
where n can be any integer number (if n = 0 we have A = B, which is trivial, this means that any angle can be coterminal with itself.)
So we can write the set as:
B = B ∈ {70° + n*360° I n ∈ Z }
The set of angles that has the same terminal arm as 70 degrees is B = B ∈ {70° + n*360°, n ∈ Z}.
We have to determine, which set of angles has the same terminal arm as 70 degrees.
According to the question,
Let, The angle A and other angle B that have the same terminal arm as A can be written as,
B = A + n × 360°
Where the value of angle A is 70 degrees.
B is the coterminal angle, and they have the same terminal,
And n is the number of integers.
Substitute the value of A in the equation,
B = 70 + n × 360°
Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.
Since the value of n is equal to 0 then A = B,
Therefore, The angles coterminal with itself is called trivial.
Hence, The set of angles that has the same terminal arm as 70 degrees is B = B ∈ {70° + n*360°, n ∈ Z}.
To know more about Terminal Arm click the link given below.
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