Answer 1 Consider the angle $\frac{\pi}{3}$ on the unit circle. To find the values of sin, cos, and tan at this angle, we use the known values: The sine of $\frac{\pi}{3}$ is: $\sin \left( \frac{\pi}{3} \right) = \frac{\sqrt{3}}{2}$ The cosine of...

Answer 1 First, recall that the unit circle is a circle with a radius of 1 centered at the origin of the coordinate plane. In the unit circle, the angle $\theta = -\pi/3$ is measured in the clockwise direction.To find the cosine of $-\pi/3$, we can...

Answer 1 We start by recognizing that the angle $-\frac{\pi}{6}$ is equivalent to rotating $\frac{\pi}{6}$ radians in the clockwise direction.On the unit circle, the point corresponding to $\frac{\pi}{6}$ radians is $(\frac{\sqrt{3}}{2},...

Answer 1 To understand what sine represents on the unit circle, let's begin with the definition of the unit circle. The unit circle is a circle with a radius of 1 centered at the origin of the coordinate system.Consider a point $P(x, y)$ on the unit...

Answer 1 We start with the unit circle formula: $x^2 + y^2 = 1$ Given $\theta = \frac{7\pi}{6}$, we need to find the cosine and sine of this angle: $\cos\left( \frac{7\pi}{6} \right) = \cos\left( \pi + \frac{\pi}{6} \right) = -\cos\left(...