Give an expression that generates all angles coterminal with each

skeexerxo175o

skeexerxo175o

Answered question

2021-12-01

Give an expression that generates all angles coterminal with each angle. Let n represent any integer. 135

Answer & Explanation

Opeance1951

Opeance1951

Beginner2021-12-02Added 26 answers

We can say for any integer n that 0 and n360 are coterminal angles 
The general expression 135+n360 gives all of the angles that are coterminal with 135 
Result: 
135+n360

RizerMix

RizerMix

Expert2023-06-10Added 656 answers

The expression can be written as:
135+360n
Here's an explanation of the expression:
- The term 135 represents the initial angle.
- The term 360 represents the full revolution around a circle.
- The term n represents any integer, which allows for the generation of multiple coterminal angles by adding or subtracting multiples of 360.
By substituting different integer values for n, you can obtain various angles that are coterminal with 135. For example, when n=0, the expression gives the original angle 135. When n=1, the expression yields 135+360=495, which is a coterminal angle. Similarly, when n=1, the expression gives 135360=225, which is also a coterminal angle.
Therefore, the expression 135+360n generates all angles coterminal with 135.
Don Sumner

Don Sumner

Skilled2023-06-10Added 184 answers

Step 1:
In this expression, n represents any integer. By substituting different integer values for n, we can generate an infinite set of angles that are coterminal with 135 degrees.
For example, when n=0, the expression becomes:
135+360·0
135
This represents the original angle of 135 degrees.
Step 2
When n=1, the expression becomes:
135+360·1
495
This angle is coterminal with 135 degrees, as it differs by a multiple of 360 degrees.
Similarly, when n=1, the expression becomes:
135+360·(1)
225
Again, this angle is coterminal with 135 degrees.
By substituting different integer values for n, we can generate an infinite set of angles that are coterminal with 135 degrees, including positive and negative angles.
Vasquez

Vasquez

Expert2023-06-10Added 669 answers

To generate all angles coterminal with 135 degrees, we can use the expression:
θ=135+360·n
Here, θ represents any angle coterminal with 135, and n represents any integer.
The term 135 represents the given angle, and adding 360·n generates additional angles that are coterminal. By multiplying 360 by n, we can cycle through all possible angles as n takes on different integer values.
Substituting different integer values for n will provide an infinite set of angles that are coterminal with 135.

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