Determine the sine and cosine of an angle $ heta $ in the unit circle in the second quadrant
Answer 1
Charlotte Davis
An angle $ \theta $ in the second quadrant of the unit circle ranges from $ 90^\circ $ to $ 180^\circ $ (or $ \frac{\pi}{2} $ to $ \pi $ radians). In this range, the sine of the angle is positive, and the cosine is negative.
For example, for $ \theta = 120^\circ $ (or $ \frac{2\pi}{3} $ radians):
$ \sin(120^\circ) = \sin(\frac{2\pi}{3}) = \frac{\sqrt{3}}{2} $
$ \cos(120^\circ) = \cos(\frac{2\pi}{3}) = -\frac{1}{2} $
Thus, the sine and cosine of an angle $ \theta $ in the second quadrant are:
$ \sin(\theta) > 0 $
$ \cos(\theta) < 0 $
Answer 2
Henry Green
An angle $ heta $ in the second quadrant ranges from $ 90^circ $ to $ 180^circ $ (or $ frac{pi}{2} $ to $ pi $ radians). Here, sine is positive and cosine is negative.
For example, for $ heta = 135^circ $ (or $ frac{3pi}{4} $ radians):
$ sin(135^circ) = sin(frac{3pi}{4}) = frac{sqrt{2}}{2} $
$ cos(135^circ) = cos(frac{3pi}{4}) = -frac{sqrt{2}}{2} $
Answer 3
Emma Johnson
In the second quadrant, angles range from $ 90^circ $ to $ 180^circ $ (or $ frac{pi}{2} $ to $ pi $ radians). Sine is positive, and cosine is negative.
For example, for $ heta = 150^circ $ (or $ frac{5pi}{6} $ radians):
$ sin(150^circ) = sin(frac{5pi}{6}) = frac{1}{2} $
$ cos(150^circ) = cos(frac{5pi}{6}) = -frac{sqrt{3}}{2} $
Start Using PopAi Today