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How do you find the coterminal with the angle 45 ?

Answer
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Hint: We are given angle as 45 , we are asked to find learning what negative in front of angle means, then we learn about coterminal angle, once we get that we work with some example to get the understanding, we learn coterminal angle using graphical representation. Then we work on our problem with angle 45 .

Complete step by step answer:
We are given as 45 , we are asked to find the coterminal angle with the angle 45 .
Firstly we will understand that the negative sign symbolic the orientation.
Now we work on our problem, we start by understanding what are coterminal angles.
coterminal angles are angles in standard position that mean angles with the initial side on the positive x-axis and have the common terminal side.
For example 30 and 330 .
If we sketch them on graph, we get better understanding
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Here 30 and 330 start from the positive axis, and have a common terminal.
So, they are coterminal angles by definition.
They can be more than 1 coterminal angle for any given angle, like for 30, apart from -330 degree, we have 390degree.
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In general, if θ is any angle whose initial side is positive x-axis then θ+n(360) is coterminal angle with θ where ‘n’ is non zero integer.
Now, we work on our problem, we have 45 , we are asked to find angle coterminal with 45.
We start by considering 45as θ , so θ=45 .
As we know that for angle θ , coterminal angle is given as θ+360n
So, for θ=45 .
Its coterminal angle is 45+n(360) .
We put n=1 , we get –
45+360×145+365=315
So, we get a coterminal angle with angle 45is 315 .

Note:
Depending upon ‘n’, we can have many other coterminal angle also graphically
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So, for 45 , 315 is coterminal.
Remember that positive or negative sign in the angle is regard to the orientation, if we measure angle in clockwise direction this it is negative, if we measure anti-clock wise then it is positive also graph way to find coterminal angle is also strong as we can clearly see whether condition of being coterminal angle are satisfied or not.
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