Find the coordinates on the unit circle corresponding to an angle theta

by zhanhongyuan | Feb 2, 2025 | Unit Circle

Home Find the coordinates on the unit circle corresponding to an angle $ heta $ Answer 1 Daniel Carter To find the coordinates on the unit circle corresponding to an angle $ theta $ , we use the parametric equations of the unit circle:$ x = cos(theta) $$ y =...

How to find the reference angle for an angle not located on the unit circle

by zhanhongyuan | Feb 2, 2025 | Unit Circle

Home How to find the reference angle for an angle not located on the unit circle Answer 1 Charlotte Davis To find the reference angle for an angle not located on the unit circle, we first need to understand that the reference angle is the smallest angle between the...

What is the value of cos(-π/3) using the unit circle?

by zhanhongyuan | Feb 2, 2025 | Unit Circle

Home What is the value of $cos(-frac{pi}{3})$ using the unit circle? Answer 1 Abigail Nelson To find the value of $cos(-frac{pi}{3})$ using the unit circle, first recognize that the cosine function is an even function. This means that:$cos(-x) =...

Find the coordinates of the point on the unit circle at which the angle is 7π/6

by zhanhongyuan | Feb 2, 2025 | Unit Circle

Home Find the coordinates of the point on the unit circle at which the angle is $ frac{7pi}{6} $ Answer 1 Lily Perez To find the coordinates of the point on the unit circle at which the angle is $ frac{7pi}{6} $, we use the following:The unit circle has the equation:$...

Find the exact coordinates of the point(s) on the unit circle where the tangent line is vertical

by zhanhongyuan | Feb 2, 2025 | Unit Circle

Home Find the exact coordinates of the point(s) on the unit circle where the tangent line is vertical Answer 1 Lucas Brown The equation of the unit circle is given by:$ x^2 + y^2 = 1 $We find the tangent line to be vertical when the derivative is undefined. Thus, we...

Find the sine and cosine of the angle when the point is (1/2, √3/2) on the unit circle

by zhanhongyuan | Feb 2, 2025 | Unit Circle

Home Find the sine and cosine of the angle when the point is ( left( frac{1}{2}, frac{sqrt{3}}{2} ight) ) on the unit circle Answer 1 Lucas Brown The coordinates ( left( frac{1}{2}, frac{sqrt{3}}{2} right) ) on the unit circle represent the cosine and sine of an...

Evaluate the integral of sin(x) * cos(x) around the unit circle

by zhanhongyuan | Feb 2, 2025 | Unit Circle

Home Evaluate the integral of $ sin(x) * cos(x) $ around the unit circle Answer 1 Sophia Williams To evaluate the integral of $ sin(x) * cos(x) $ around the unit circle, we can use the double-angle identity: $ sin(x) cos(x) = frac{1}{2} sin(2x) $Now, we need to...

Find the terminal point on the unit circle for an angle of pi/6 radians

by zhanhongyuan | Feb 2, 2025 | Unit Circle

Home Find the terminal point on the unit circle for an angle of $ frac{pi}{6} $ radians Answer 1 Emily Hall To find the terminal point on the unit circle for an angle of $ frac{pi}{6} $ radians, we use the unit circle definition:The coordinates are given by $ ( cos(...

Identify the sine and cosine values for the angle π/4 on the unit circle

by zhanhongyuan | Feb 2, 2025 | Unit Circle

Home Identify the sine and cosine values for the angle $ frac{pi}{4} $ on the unit circle. Answer 1 Michael Moore To find the sine and cosine values for the angle $ frac{pi}{4} $ on the unit circle, we use the definitions of sine and cosine:$ sinleft(frac{pi}{4}right)...

Find the cosine of the angle at 3π/4 radians on the unit circle

by zhanhongyuan | Feb 2, 2025 | Unit Circle

Home Find the cosine of the angle at $ frac{3π}{4} $ radians on the unit circle Answer 1 Sophia Williams The unit circle helps us find the cosine of an angle. For an angle of $ frac{3π}{4} $ radians:The reference angle is $ x0crac{π}{4} $, and in the second quadrant,...