Question

6 find the reference angle.
a) \\(\frac{17\pi}{15}\\)
b) \\(299^\circ)
c) \\(2.8\\)

Explanation:

Step1: Reduce angle to 0-2π

$\frac{17\pi}{15} - 2\pi = \frac{17\pi}{15} - \frac{30\pi}{15} = -\frac{13\pi}{15}$, equivalent to $\frac{17\pi}{15}$ (in Q3).

Step2: Calculate Q3 reference angle

$\frac{17\pi}{15} - \pi = \frac{17\pi}{15} - \frac{15\pi}{15} = \frac{2\pi}{15}$
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Step1: Identify quadrant of 299°

$270^\circ < 299^\circ < 360^\circ$, so Q4.

Step2: Calculate Q4 reference angle

$360^\circ - 299^\circ = 61^\circ$
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Step1: Convert radians to 0-2π range

$2\pi \approx 6.28$, so $2.8$ radians is in Q2.

Step2: Calculate Q2 reference angle

$\pi - 2.8 \approx 3.14 - 2.8 = 0.34$ radians

Answer:

a) $\frac{2\pi}{15}$
b) $61^\circ$
c) $\approx 0.34$ radians