Degrees and Radians Conversion

Vocabulary flashcards covering methods, formulas, and sign rules for converting between degrees and radians based on section 6.1 homework notes.

Degrees to Radians conversion formula

$$\text{Degree} \left(\frac{\pi\text{ radian}}{180^\circ}\right)$$

Radians to Degrees conversion formula

$$\text{Radian} \left(\frac{180^\circ}{\pi}\right) = \text{decimal / non decimal degree}$$

If the degree is negative what will the radian be

If it is a negative degree, it will result in a negative radian, and vice versa.

-30 degrees is $-\frac{\pi}{6}$

Radian conversion of $-40^\circ$ (can cancel out)

$\frac{-2\pi}{9}\text{ radian}$, obtained by simplifying $-40^\circ \left(\frac{\pi\text{ radian}}{180^\circ}\right)$ to keep $\pi$ in the answer.

Radian conversion of $73^\circ$

$\frac{73\pi}{180}\text{ radian}$ (or $1.27\text{ radian}$), obtained by evaluating $73^\circ \left(\frac{\pi\text{ radian}}{180^\circ}\right)$ as a decimal when the fraction cannot be canceled out.

Solving to decimals

A degree-to-radian conversion technique used when terms cannot be canceled out,

solving the entire expression to obtain decimals as shown in $73^\circ \left(\frac{\pi\text{ radian}}{180^\circ}\right) = \frac{73\pi}{180}\text{ radian} = 1.27\text{ radian}$.

Radians to Degrees conversion

The process of converting radians to a decimal

or non-decimal degree using the formula $\text{Radian} \left(\frac{180^\circ}{\pi}\right) = \text{decimal / non decimal degree}$.