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Answer 1 Consider a point on the unit circle in the complex plane, given by the complex number $z = e^{i\theta}$ where $\theta$ is the angle in radians from the positive x-axis.The coordinate of this point can be written as $(\cos\theta,...
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Answer 1 To find the sine and cosine of the angle $\theta = \frac{5\pi}{6}$ using the unit circle: 1. Locate the angle $\theta = \frac{5\pi}{6}$ on the unit circle. This angle is in the second quadrant. 2. The reference angle for $\theta =...
Answer 1 To find the angle θ corresponding to the point $(\frac{1}{2}, \frac{\sqrt{3}}{2})$ on the unit circle, we start with the basic trigonometric relationships: $ \cos \theta = x $ $ \sin \theta = y $ Given $ x = \frac{1}{2} $ and $ y =...
Answer 1 $120\ degrees\ is\ in\ the\ second\ quadrant.\ The\ reference\ angle\ is\ 180 - 120 = 60\ degrees.$$In\ the\ second\ quadrant,\ \cos(\theta)\ is\ negative.$$\cos(60\ degrees) = \frac{1}{2},\ so\ \cos(120\ degrees) = -\frac{1}{2}.$Answer 2...