Find the coordinates on the unit circle corresponding to an angle of θ

by zhanhongyuan | Feb 7, 2025 | Unit Circle

Home Find the coordinates on the unit circle corresponding to an angle of $ heta $ Answer 1 Daniel Carter To find the coordinates on the unit circle for an angle $ theta $, we use the trigonometric functions sine and cosine. The coordinates are given by:n $ (x, y) =...

Find the points on the unit circle where the secant of the angle is equal to 2, and prove their coordinates

by zhanhongyuan | Feb 7, 2025 | Unit Circle

Home Find the points on the unit circle where the $ sec( heta) = 2 $, and prove their coordinates. Answer 1 Ava Martin To find points on the unit circle where $ sec(theta) = 2 $, recall that: $ sec(theta) = frac{1}{cos(theta)} $ Thus, we need: $ frac{1}{cos(theta)} =...

Determine the coordinates of the points where the unit circle intersects the line y = 2x + 1

by zhanhongyuan | Feb 7, 2025 | Unit Circle

Home Determine the coordinates of the points where the unit circle intersects the line $ y = 2x + 1 $ Answer 1 Michael Moore First, recall the equation of the unit circle: $ x^2 + y^2 = 1 $Substitute $ y = 2x + 1 $ into the unit circle equation: $ x^2 + (2x + 1)^2 = 1...

Find the angle in degrees for which the sine and cosine values are equal on the unit circle

by zhanhongyuan | Feb 7, 2025 | Unit Circle

Home Find the angle in degrees for which the $sin$ and $cos$ values are equal on the unit circle. Answer 1 Henry Green To find the angle $theta$ in degrees for which $sin(theta) = cos(theta)$ on the unit circle, start by equating the two trigonometric functions: $...

Find the coordinates of the point on the unit circle where the terminal side of the angle 5π/6 intersects the circle

by zhanhongyuan | Feb 7, 2025 | Unit Circle

Home Find the coordinates of the point on the unit circle where the terminal side of the angle $ frac{5pi}{6} $ intersects the circle. Answer 1 Sophia Williams To find the coordinates of the point where the terminal side of the angle $ frac{5pi}{6} $ intersects the...

Find the exact values of sin(θ), cos(θ), and tan(θ) for θ = 3π/4

by zhanhongyuan | Feb 7, 2025 | Unit Circle

Home Find the exact values of $ sin( heta) $, $ cos( heta) $, and $ an( heta) $ for $ heta = frac{3pi}{4} $ Answer 1 Chloe Evans Consider the angle $ theta = frac{3pi}{4} $, which is in the second quadrant.Using the unit circle, we know:$ sin(frac{3pi}{4}) = sin(pi...

Find the exact trigonometric values of cos(5π/6) and sin(5π/6) from the unit circle

by zhanhongyuan | Feb 7, 2025 | Unit Circle

Home Find the exact trigonometric values of $cosleft(frac{5pi}{6} ight)$ and $sinleft(frac{5pi}{6} ight)$ from the unit circle Answer 1 Olivia Lee To find the exact values of $cosleft(frac{5pi}{6}right)$ and $sinleft(frac{5pi}{6}right)$, we refer to the unit circle....

Find the coordinates of a point on the unit circle at an angle of π/6

by zhanhongyuan | Feb 7, 2025 | Unit Circle

Home Find the coordinates of a point on the unit circle at an angle of $ frac{pi}{6} $ Answer 1 Ava Martin To find the coordinates of a point on the unit circle at an angle of $ frac{pi}{6} $, we use the fact that the coordinates are given by $ ( cos(theta),...

Calculate the area of the shaded region in a unit circle with central angles

by zhanhongyuan | Feb 7, 2025 | Unit Circle

Home Calculate the area of the shaded region in a unit circle with central angles $ heta $ and $ alpha $ Answer 1 Samuel Scott Let’s calculate the area of the shaded region in a unit circle with central angles $ theta $ and $ alpha $.The area of a sector of a circle...

Find the coordinates on the unit circle for the angles

by zhanhongyuan | Feb 7, 2025 | Unit Circle

Home Find the coordinates on the unit circle for the angles Answer 1 Lily Perez Find the coordinates on the unit circle for the angle $ theta = frac{pi}{4} $:The coordinates are given by $ (cos(theta), sin(theta)) $.For $ theta = frac{pi}{4} $:$...