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Convert the following angle from degrees to radians. Express your answer in simplest form.

345^(@)
Answer:

Convert the following angle from degrees to radians. Express your answer in simplest form. $\newline$ $345^{\circ}$ $\newline$ Answer:

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Csc, sec, and cot of special angles

Full solution

Q. Convert the following angle from degrees to radians. Express your answer in simplest form.

\newline

345^{\circ}

\newline

Answer:

Set up conversion factor: To convert degrees to radians, we use the conversion factor that π radians is equivalent to $180$ degrees. Therefore, we can set up the conversion as follows: $\newline$ $\text{radians} = \text{degrees} \times \left( \frac{\pi \text{ radians}}{180 \text{ degrees}} \right)$
Plug in given angle: Now, we plug in the given angle of $345$ degrees into the conversion formula: $\newline$ $\text{radians} = 345^\circ \times \left( \frac{\pi}{180} \right)$
Simplify expression: Next, we simplify the expression by canceling out any common factors between the numerator and the denominator. In this case, both $345$ and $180$ can be divided by $15$ : $\newline$ $\text{radians} = \frac{345}{15} \times \left( \frac{\pi}{\frac{180}{15}} \right)$ $\newline$ $\text{radians} = 23 \times \left( \frac{\pi}{12} \right)$
Multiply to get radians: Finally, we multiply the two numbers together to get the angle in radians: $\newline$ $\text{radians} = 23 \times \frac{\pi}{12}$ $\newline$ $\text{radians} = \frac{23\pi}{12}$ $\newline$ This is the simplest form of the angle in radians.

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