by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Calculate the tangent of an angle when given the sine and cosine values in the unit circle Answer 1 Charlotte Davis To find the tangent of an angle in the unit circle when given the sine and cosine values, we use the formula:$ tan(theta) =...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Determine the values of $ cos( heta) $ and $ sin( heta) $ given that the point $ (x, y) $ is on the unit circle Answer 1 Matthew Carter Given that $ (x, y) $ is on the unit circle, we know:$ x^2 + y^2 = 1 $Using the definitions of the trigonometric functions on...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Define a unit circle and prove that any point $(x, y)$ on the unit circle satisfies the equation $x^2 + y^2 = 1$. Answer 1 Mia Harris A unit circle is a circle with a radius of 1 unit, centered at the origin (0,0) in the Cartesian coordinate system. To prove that...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Find the exact value of $ sin(frac{pi}{4}) $ on the unit circle. Answer 1 Alex Thompson To find the exact value of $ sin(frac{pi}{4}) $ on the unit circle, we recognize that $ frac{pi}{4} $ is equivalent to $ 45^{circ} $. On the unit circle, the coordinates for $...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Find the value of $ sin( heta) $ and $ cos( heta) $ where $ heta = frac{pi}{3} $ using the unit circle. Answer 1 John Anderson To find the values of $ sin(theta) $ and $ cos(theta) $ where $ theta = frac{pi}{3} $, we use the unit circle.On the unit circle, the...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Find the value of $ an(x) $ for $ x = frac{pi}{4} $ Answer 1 Alex Thompson To find the value of $ tan(x) $ when $ x = frac{pi}{4} $, we use the unit circle chart.For $ x = frac{pi}{4} $, the coordinates on the unit circle are (frac{sqrt{2}}{2},...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Explain the concept of a unit circle, including its importance in trigonometry and how it relates to the coordinates of points on the circle. Answer 1 Abigail Nelson A unit circle is a circle with a radius of 1, centered at the origin of a coordinate system. The...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Find the angle in degrees corresponding to $frac{7pi}{6}$ radians on the unit circle Answer 1 Samuel Scott To convert $frac{7pi}{6}$ radians to degrees, we use the conversion factor: $ 180^{circ} = pi text{ radians} $ Thus, $ frac{7pi}{6} times...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Find the coordinates on the unit circle where $ an( heta) = 1 $ Answer 1 Ella Lewis To find the coordinates on the unit circle where $ tan(theta) = 1 $, we need to determine the angles $theta $ for which this condition holds. We know that:$ tan(theta) = frac...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Find the sine value at $ frac{pi}{3} $ on the unit circle Answer 1 Samuel Scott To find the sine value at $ frac{pi}{3} $ on the unit circle, we use the unit circle definition. The angle $ frac{pi}{3} $ is equivalent to 60 degrees.On the unit circle, the sine...