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 coordinates where the line $ y = 1 $ intersects the unit circle, we start by recalling the equation of the unit circle:$ x^2 + y^2 = 1 $Substituting $ y = 1 $ into the unit circle equation, we get:$ x^2 + 1^2 = 1 $Simplifying,$...
Answer 1 The equation of the unit circle is given by: $ x^2 + y^2 = 1 $ To find the tangent line at the point $\left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right)$, we need to determine the slope. Differentiating implicitly: $ 2x \frac{dx}{dt} + 2y...
Answer 1 First, we need to convert $ 30^{\circ} $ to radians: $ 30^{\circ} = \frac{\pi}{6} $ Using the unit circle, the coordinates for $ \frac{\pi}{6} $ are $ \left( \frac{\sqrt{3}}{2}, \frac{1}{2} \right) $ From this, we can find: $ \sin...
Answer 1 Given that $\sin(θ) = \frac{3}{5}$ and $θ$ is in the first quadrant, we can find $\cos(θ)$ using the Pythagorean identity:$\sin^2(θ) + \cos^2(θ) = 1$Plugging in the given value:$\left(\frac{3}{5}\right)^2 + \cos^2(θ) = 1$$\frac{9}{25} +...
Answer 1 To find the values of $ \tan(\theta) $ at various angles and verify using the unit circle, we consider the following angles: $ \theta = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4} $1. For $ \theta = \frac{\pi}{4} $:$...
Answer 1 To determine the coordinates of a point on the unit circle where the tangent line has a slope of $\frac{3}{4}$, we start with the equation of the unit circle:$x^2 + y^2 = 1$The slope of the tangent line at a point $(x, y)$ on the circle can...