Reference Angle
- Thread starter lewch45
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I will assume that "reference angle" means "the angle between 0° and 360° the corresponds with the given angle". If this is not (equivalent to) the definition you're supposed to be using, please reply with corrections. Thank you.
Under the above assumption, you can find equivalent angles by adding or subtracting "once around" (2pi or 360°, depending on whether you're in radians or degrees) as often as you need, until you get something that is between 0 and 2pi (or 0° and 360°).
1) Hint: (18/7)pi = (14/7 + 4/7)pi = (2 + 4/7)pi = 2pi + (4/7)pi
How many "once around's" should you add to or subtract from this to leave something that is between 0 and 2pi?
2) Hint: 2(360°) = 720°
Eliz.
Under the above assumption, you can find equivalent angles by adding or subtracting "once around" (2pi or 360°, depending on whether you're in radians or degrees) as often as you need, until you get something that is between 0 and 2pi (or 0° and 360°).
1) Hint: (18/7)pi = (14/7 + 4/7)pi = (2 + 4/7)pi = 2pi + (4/7)pi
How many "once around's" should you add to or subtract from this to leave something that is between 0 and 2pi?
2) Hint: 2(360°) = 720°
Eliz.
pka
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We can ‘throw away’ multiples of \(\displaystyle 2\pi\) and of \(\displaystyle 360^0\)
\(\displaystyle \frac{{18\pi }}{7} = \frac{{4\pi }}{7} + \frac{{14\pi }}{7}\) hence the reference angle is \(\displaystyle \frac{{4\pi }}{7}\).
Also \(\displaystyle - 650^o = 70^o - 2(360^o )\) so the reference angle is \(\displaystyle 70^o\)
\(\displaystyle \frac{{18\pi }}{7} = \frac{{4\pi }}{7} + \frac{{14\pi }}{7}\) hence the reference angle is \(\displaystyle \frac{{4\pi }}{7}\).
Also \(\displaystyle - 650^o = 70^o - 2(360^o )\) so the reference angle is \(\displaystyle 70^o\)