Explore the unit circle and its relationship to angles, radians, trigonometric ratios, and coordinates in the coordinate plane.
The page you requested could not be found. Try refining your search, or use the navigation above to locate the post.
Start Using PopAi Today
Suggested Content
More >
Answer 1 To find the radius of a circle when given its circumference, use the formula for circumference:$C = 2\pi r$We are given that the circumference $C = 31.4$ units. Substitute $C$ into the formula and solve for $r$:$31.4 = 2\pi r$Divide both...
Answer 1 To find the equation of a unit circle centered at the origin, we need to remember that a unit circle has a radius of 1. The standard form of a circle's equation is:$ (x - h)^2 + (y - k)^2 = r^2 $Where (h, k) is the center of the circle and r...
Answer 1 To find the secant value, we first need to know the cosine value of the given angle on the unit circle. The angle $\frac{\pi}{3}$ corresponds to an angle of $60^\circ$. On the unit circle, the cosine of $\frac{\pi}{3}$ is $\frac{1}{2}$. The...
Answer 1 Given an angle of $\frac{5\pi}{6}$ radians, we need to find the coordinates of the point on the unit circle corresponding to this angle. First, note that $\frac{5\pi}{6}$ radians lies in the second quadrant. The reference angle for...
Answer 1 Given the angle $ \theta = 30^{\circ} $, we need to find $ \sin(\theta) $ using the unit circle. On the unit circle, the coordinates of the point corresponding to $ 30^{\circ} $ are $ \left( \frac{\sqrt{3}}{2}, \frac{1}{2} \right) $. The...
Answer 1 To understand the unit circle at an advanced level, consider the problem of determining the exact value of trigonometric functions given a point on the unit circle. Suppose a point $P$ on the unit circle corresponds to an angle $\theta$....