Find the cosine of the angle formed by the complex number in the unit circle

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Find the cosine of the angle formed by the complex number in the unit circle Answer 1 Michael Moore Given a complex number $z = cos(theta) + isin(theta)$ on the unit circle, find the cosine of the angle $theta$.We know that for a complex number on the unit...

Find the sine and cosine of 135 degrees using the unit circle

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home $ ext{Find the sine and cosine of } 135^circ ext{ using the unit circle.}$ Answer 1 Thomas Walker $135^circ$ is in the second quadrant. The reference angle is $180^circ – 135^circ = 45^circ$. The sine and cosine values for $45^circ$ are $ frac{1}{sqrt{2}}$...

Find the coordinates of the point on the unit circle at an angle of \( \frac{\pi}{3} \) radians

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Find the coordinates of the point on the unit circle at an angle of $ frac{pi}{3} $ radians. Answer 1 Abigail Nelson To find the coordinates of the point on the unit circle at an angle of $ frac{pi}{3} $ radians, we use the formula for the coordinates on the unit...

Find the circumference of a circle with a diameter of 10 cm

by zhanhongyuan | Feb 13, 2025 | Math

Home Find the circumference of a circle with a diameter of $10 ext{ cm}$. Answer 1 Charlotte Davis To find the circumference of a circle, we use the formula:$C = pi d$Given the diameter $d = 10 text{ cm}$, we substitute into the formula:$C = pi times 10$Therefore, the...

Determine the coordinates on the unit circle for the angle whose cosine is -2/3

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Determine the coordinates on the unit circle for the angle whose cosine is $-frac{2}{3}$ Answer 1 Emily Hall To find the coordinates on the unit circle for the angle whose cosine is $-frac{2}{3}$, we use the Pythagorean identity: $cos^2theta + sin^2theta = 1$...

Find the slope of the tangent line to the unit circle at the point (1/2, sqrt(3)/2)

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Find the slope of the tangent line to the unit circle at the point $left( frac{1}{2}, frac{sqrt{3}}{2} ight)$. Answer 1 Henry Green To find the slope of the tangent line to the unit circle at a given point, we need to differentiate the equation of the unit...

Find the cosine of an angle of \(\frac{\pi}{3}\) radians on the unit circle

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Find the cosine of an angle of $frac{pi}{3}$ radians on the unit circle. Answer 1 Lucas Brown To find the cosine of an angle of $frac{pi}{3}$ radians on the unit circle, we need to look at the coordinates of the point where the terminal side of the angle...

Find the coordinates of a point and the corresponding angle on the unit circle given the sine value, and prove if the cosine value meets the trigonometric identity

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Find the coordinates of a point and the corresponding angle on the unit circle given the sine value, and prove if the cosine value meets the trigonometric identity. Answer 1 Christopher Garcia Given the sine value $sin(theta) = frac{3}{5}$ on the unit circle,...

Find the value of cos(θ) on the unit circle when θ = 60°

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Find the value of $cos( heta)$ on the unit circle when $ heta = 60°$. Answer 1 Thomas Walker To solve for $cos(60°)$, we can use the unit circle, where $theta$ represents the angle from the positive x-axis.On the unit circle, the coordinates of a point at an...

Find the cosine and sine values of an angle in the unit circle

by zhanhongyuan | Feb 13, 2025 | Unit Circle

Home Find the cosine and sine values of an angle in the unit circle Answer 1 Emma Johnson Given an angle of ( frac{5pi}{4} ) radians, determine the cosine and sine values using the unit circle. First, locate the angle ( frac{5pi}{4} ) on the unit circle. This angle is...