Question

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measuring in radians exit ticket
degrees to radians
convert the following from degrees to radians. be sure to show all your work!
a. $15^\circ$
b. $60^\circ$

radians to degrees
convert the following from radians to degrees. be sure to show all your work!
a. $\frac{4\pi}{3}$
b. $\frac{11\pi}{6}$

rate your confidence on todays learning objective, where 0 is
ot at all\ and 10 is \perfectly understand\.
i understand what a radian is.
0 2 4 6 8 10
i can convert between degrees and radians.
0 2 4 6 8 10

Explanation:

Step1: Degrees to radians formula

To convert degrees to radians, multiply by $\frac{\pi}{180^\circ}$.

a. Convert $15^\circ$ to radians

$15^\circ \times \frac{\pi}{180^\circ} = \frac{15\pi}{180} = \frac{\pi}{12}$

b. Convert $60^\circ$ to radians

$60^\circ \times \frac{\pi}{180^\circ} = \frac{60\pi}{180} = \frac{\pi}{3}$

Step2: Radians to degrees formula

To convert radians to degrees, multiply by $\frac{180^\circ}{\pi}$.

a. Convert $\frac{4\pi}{3}$ to degrees

$\frac{4\pi}{3} \times \frac{180^\circ}{\pi} = \frac{4 \times 180^\circ}{3} = 240^\circ$

b. Convert $\frac{11\pi}{6}$ to degrees

$\frac{11\pi}{6} \times \frac{180^\circ}{\pi} = \frac{11 \times 180^\circ}{6} = 330^\circ$

Answer:

Degrees to Radians:

a. $\frac{\pi}{12}$
b. $\frac{\pi}{3}$

Radians to Degrees:

a. $240^\circ$
b. $330^\circ$

(Note: The confidence rating section is a self-assessment for the learner, with no fixed academic answer.)