by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Evaluate the integral of $ cos^3(x)sin(x) $ with respect to $ x $ Answer 1 Joseph Robinson To evaluate the integral of $ cos^3(x)sin(x) $ with respect to $ x $, we use a substitution method:Let $ u = cos(x) $, then $ du = -sin(x) dx $. Consequently:$ int...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Determine the angle in radians of the point on the unit circle in the first quadrant with an $x$-coordinate of $frac{1}{2}$ Answer 1 Isabella Walker To find the angle in radians with an $x$-coordinate of $frac{1}{2}$ in the first quadrant, we use the unit circle...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Determine the cosine of an angle given in radians and convert it to degrees Answer 1 Amelia Mitchell Given an angle $ theta = frac{7pi}{6} $ radians, we need to determine its cosine and convert the angle to degrees.nFirst, convert the angle to degrees:n n$ theta...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the value of $ sec( heta) $ for $ heta $ in the unit circle Answer 1 Lucas Brown To find the value of $ sec(theta) $ for $ theta $ in the unit circle, we need to recall the definition of secant. The secant function is the reciprocal of the cosine function: $...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the sine of an angle whose terminal side passes through the point $left(frac{sqrt{3}}{2}, -frac{1}{2} ight)$ on the unit circle Answer 1 Amelia Mitchell To find the sine of the angle, we need to identify the y-coordinate of the given point...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Determine the quadrant for the given angle $ heta $ on a unit circle Answer 1 Lucas Brown The angle $ theta = 45^circ $ is in the first quadrant. Answer 2 William King The angle $ heta = 135^circ $ is in the second quadrant. Answer 3 Lily Perez The angle $ heta =...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the secant line to the unit circle that is equidistant from the $x$-axis Answer 1 William King To find the secant line to the unit circle that is equidistant from the $x$-axis, we use the equation of the unit circle $ x^2 + y^2 = 1 $and the general equation...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Determine the exact values of sine and cosine for the angle $ frac{pi}{4} $ using the unit circle Answer 1 Matthew Carter To find the exact values of sine and cosine for the angle $ frac{pi}{4} $, we use the unit circle.For $ theta = frac{pi}{4} $, the...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Identify the coordinates of specific angles on the unit circle. Answer 1 Olivia Lee To find the coordinates of specific angles on the unit circle, remember that the unit circle has a radius of 1.For the angle $theta = frac{pi}{4}$, the coordinates...
by zhanhongyuan | Feb 6, 2025 | Unit Circle
Home Find the area of a sector in a unit circle with a central angle of $ heta $ radians Answer 1 Joseph Robinson The formula to find the area of a sector in a unit circle is:$ A = frac{1}{2} theta $where $ theta $ is the central angle in radians.For example, if $...