# How to find Reference Angles from the Calculator

Reference angles are used to find the acute angle measure (between $$0$$ and $$90$$ degrees) that corresponds to a given angle in standard position (between $$0$$ and $$360$$ degrees). They are particularly useful when working with trigonometric functions and their inverses on a calculator.

## Step-by-step to find reference angles and the Calculator

Here are the general steps to follow to find the reference angle using a calculator:

1. Input the given angle in standard position into the calculator.
2. Press the “mod” or “modulo” button on the calculator to find the remainder when the angle is divided by $$360$$. This will give you the reference angle.

For example, if you want to find the reference angle for an angle of $$450$$ degrees, you would input $$450$$ and then press the “mod” button, and the calculator would display $$90$$.

It’s important to note that the reference angle is always acute, meaning it is always less than $$90$$ degrees.

When working with trigonometric functions such as sine, cosine and tangent, it’s important to be aware of the periodicity of these functions, which is $$2pi$$ or $$360$$ degrees. This means that the values of these functions repeat after every $$2pi$$ or $$360$$ degrees, so it’s important to use the reference angle in order to get the correct value of the function.

Some calculators also have built-in functions or buttons that can be used to find the reference angle directly. For example, some calculators have a “Quadrant” button that can be used to find the quadrant in which an angle lies, which can then be used to determine the reference angle.

It’s always a good idea to refer to the calculator’s user manual for specific instructions on how to find the reference angle using the calculator’s built-in functions.

In summary, reference angles are useful to simplify trigonometric problems, they help to determine the correct value of a trigonometric function by reducing the given angle to a value between $$0$$ and $$90$$ degrees. To find the reference angle using a calculator, it’s important to be aware of the periodicity of trigonometric functions, and use the mod button or built-in functions if available.

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