Question

For an angle 136 degrees, find the following find The reference angles in radians

Answer 1

Answer:

$136$ degrees is approximately $2.373$ in radiance.

$136$ degrees is exactly $\frac{34 \pi}{45}$ in radiance.

Step-by-step explanation:

Let $r$ be radiance.

Let $d$ be degrees ($^{\circ}$).

Recall:

$d = \frac{\pi}{180}r$

Writing $136$ degrees in radiance:

$136d \\ 136d \cdot \frac{\frac{\pi}{180}r}{d} \\ 136 \cdot \frac{\pi}{180}r \\ \frac{136 \pi}{180}r \\ \frac{34 \pi}{45}r \\ 0.7\overline{5} \pi r$

$136$ degrees is $0.7\overline{5} \pi$ in radiance. If we estimate $\pi$ to be $3.14$, $0.7\overline{5} \pi \approx 2.373$.

Answer 2

Step-by-step explanation:

$radians = \frac{2\pi}{360} \times 136$

$= \frac{\pi}{180} \times 136$

$= \frac{34\pi}{45}$