What does the sine function represent on the unit circle?

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home What does the $ sin $ function represent on the unit circle? Answer 1 Chloe Evans On the unit circle, the sine function $ sin(theta) $ represents the y-coordinate of a point on the circle corresponding to the angle $ theta $ measured from the positive...

Determine the values of trigonometric functions for specific angles on the unit circle

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Determine the values of trigonometric functions for specific angles on the unit circle Answer 1 Sophia Williams Given the angle $ theta = frac{5pi}{4} $ radians, find the values of $ sin(theta) $, $ cos(theta) $, and $ tan(theta) $. The coordinates of $...

Find the value of arcsin(1/2) using the unit circle

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Find the value of $ arcsin(frac{1}{2}) $ using the unit circle. Answer 1 Isabella Walker To find the value of $ arcsin(frac{1}{2}) $ using the unit circle, we need to determine the angle whose sine is $ frac{1}{2} $.On the unit circle, the sine of an angle is the...

Determine the coordinates of a point on the unit circle where the sine value is 1/2 and the tangent value is positive

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Determine the coordinates of a point on the unit circle where the $sin( heta) = frac{1}{2}$ and the $ an( heta)$ value is positive. Answer 1 Charlotte Davis To find the coordinates where $sin(theta) = frac{1}{2}$ and $tan(theta)$ is positive, we analyze the unit...

Find the value of tan(θ) using the unit circle when θ is in the third quadrant

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Find the value of $ an(θ) $ using the unit circle when $ θ $ is in the third quadrant Answer 1 Alex Thompson To find the value of $ tan(θ) $ using the unit circle, we need to determine the coordinates where $ θ $ intersects the unit circle in the third...

Find the cosine of the angle pi/4 on the unit circle

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Find the cosine of the angle $ frac{pi}{4} $ on the unit circle Answer 1 William King The unit circle defines the standard positions and values of trigonometric functions. For the angle $ frac{pi}{4} $ (or 45 degrees), we use the unit circle definition:The...

Determine the coordinates of a point in the first quadrant of the unit circle given its angle

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Determine the coordinates of a point in the first quadrant of the unit circle given its angle $ heta $ Answer 1 Daniel Carter To determine the coordinates of a point in the first quadrant on the unit circle given its angle $ theta $, we use the trigonometric...

Find the exact value of the inverse trig function expressions

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Find the exact value of the inverse trig function expressions Answer 1 Maria Rodriguez Consider the expression $ sin^{-1}left( frac{sqrt{3}}{2} right) $. We know that $ sinleft( frac{pi}{3} right) = frac{sqrt{3}}{2} $. Therefore, $ sin^{-1}left( frac{sqrt{3}}{2}...

Find the points where the ellipse intersects the empty unit circle

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Find the points where the ellipse intersects the empty unit circle Answer 1 Lucas Brown To find the points where the ellipse intersects the empty unit circle, we start with the equations of the ellipse and the empty unit circle:Ellipse: $x0crac{x^2}{a^2} +...

Determine the points of intersection between the unit circle and the curve y = x^3 – x

by zhanhongyuan | Feb 3, 2025 | Unit Circle

Home Determine the points of intersection between the unit circle and the curve $ y = x^3 - x $ Answer 1 Christopher Garcia To find the points of intersection between the unit circle $x^2 + y^2 = 1$ and the curve $y = x^3 – x$, we substitute $y$ from the second...