Science

Answer 1 To solve this problem, we first need to understand the transformation of the coordinate system.In the standard unit circle, an angle of $\frac{5\pi}{6}$ radians would correspond to the point $(-\cos(\frac{\pi}{6}),...

Answer 1 Let's consider the angle $ \theta = \frac{7\pi}{6}$. First, we determine the reference angle. Since $\frac{7\pi}{6}$ is in the third quadrant, we find the reference angle by subtracting $\pi$: $ \theta_{ref} = \frac{7\pi}{6} - \pi =...

Answer 1 Given the angle $\theta = \frac{5\pi}{6}$ radians, we need to find the coordinates of the point on the unit circle.On the unit circle, the coordinates of a point at an angle $\theta$ are $(\cos(\theta), \sin(\theta))$.Therefore,$x =...

Answer 1 First, let's write the equation of the unit circle: $x^2 + y^2 = 1.$ Since $y = 2x$, we can substitute $2x$ for $y$ in the unit circle equation: $x^2 + (2x)^2 = 1.$ This simplifies to: $x^2 + 4x^2 = 1$ $5x^2 = 1$ $x^2 = \frac{1}{5}$ $x = \pm...

Answer 1 To find the sine, cosine, and tangent of an angle of 45 degrees on the unit circle:The coordinates of the point at $45^\circ$ on the unit circle are $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$.Therefore, $\sin(45^\circ) =...

Answer 1 To find the coordinates of the point where the angle $\theta = 45^\circ$ intersects the unit circle, we use the fact that the unit circle has a radius of 1. The coordinates on the unit circle are given by $(\cos \theta, \sin \theta)$.$\cos...