find the reference number for each value of t.\n(a) ( t=\frac{5 pi}{7} )\n( \frac{2 pi}{7} )\n(b) (…
find the reference number for each value of t.\n(a) ( t=\frac{5 pi}{7} )\n( \frac{2 pi}{7} )\n(b) ( t=-\frac{7 pi}{9} )\n( \frac{2 pi}{9} )\n(c) ( t=-3 )\n(d) ( t=5 )
Answer
Explanation:
Step1: Determine the quadrant for (t = - 3)
Since (\pi\approx3.14), then (-3) is equivalent to (2\pi - 3\approx6.28 - 3 = 3.28). And (\pi<3.28<\frac{3\pi}{2}), so (t=-3) is in the third - quadrant. The formula for the reference number (\overline{t}) when (t) is in the third - quadrant is (\overline{t}=t-\pi). (\overline{t}=2\pi - 3-\pi=\pi - 3\approx3.14 - 3=0.14)
Step2: Determine the quadrant for (t = 5)
Since (2\pi\approx6.28), then (5) is in the fourth - quadrant ((\frac{3\pi}{2}\approx4.71<5<2\pi)). The formula for the reference number (\overline{t}) when (t) is in the fourth - quadrant is (\overline{t}=2\pi - t) (\overline{t}=2\pi - 5\approx6.28 - 5 = 1.28)
Answer:
(c) (\pi - 3) (d) (2\pi - 5)