Find the values of sin, cos, and tan for angles that satisfy the equation 2sin(x)cos(x) = 1

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Find the values of $sin$, $cos$, and $ an$ for angles that satisfy the equation $2sin(x)cos(x) = 1$ Answer 1 Emily Hall First, recognize that $2sin(x)cos(x) = sin(2x)$. Thus, the equation becomes: $sin(2x) = 1$ The solution for $sin(2x) = 1$ occurs at: $2x =...

Find the coordinates of a point on the negative unit circle given a specific angle

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Find the coordinates of a point on the negative unit circle given a specific angle $ heta $ Answer 1 Joseph Robinson To find the coordinates of a point on the negative unit circle given a specific angle $ theta $, we use the equation of the unit circle: $ x^2 +...

Determine the points on the negative unit circle where the tangent line is vertical

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Determine the points on the negative unit circle where the tangent line is vertical Answer 1 Michael Moore The negative unit circle is described by the equation:$ x^2 + y^2 = -1 $To find where the tangent line is vertical, we need to find the points where the...

Prove that the sum of the squares of the sine and cosine functions on the unit circle equals 1

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Prove that the sum of the squares of the $sin$ and $cos$ functions on the unit circle equals 1. Answer 1 Samuel Scott On the unit circle, any point is represented as $(cos(theta), sin(theta))$, where $theta$ is the angle formed with the positive x-axis.According...

Find the coordinates of the point on the unit circle for angle π/3

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Find the coordinates of the point on the unit circle for angle $ frac{pi}{3} $ Answer 1 Emma Johnson For the angle $ frac{pi}{3} $ on the unit circle, the coordinates are found using the sine and cosine functions.The x-coordinate is:$ cosleft( frac{pi}{3} right)...

Determine the value of cos(7π/6) using the unit circle

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Determine the value of $ cosleft(frac{7pi}{6} ight) $ using the unit circle Answer 1 Lily Perez To determine the value of $ cosleft(frac{7pi}{6}right) $ using the unit circle, we need to locate the angle $ frac{7pi}{6} $ in radians. This angle is in the third...

Determine the sine and cosine values for an angle of 5π/6 radians on the unit circle

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Determine the sine and cosine values for an angle of $ frac{5pi}{6} $ radians on the unit circle Answer 1 Emily Hall To find the sine and cosine of $ frac{5pi}{6} $ on the unit circle, we use the reference angle and the fact that it lies in Quadrant II:The...

Express the coordinates of key points on the unit circle in terms of trigonometric functions

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Express the coordinates of key points on the unit circle in terms of trigonometric functions Answer 1 Lucas Brown To express the coordinates of key points on the unit circle in terms of trigonometric functions, remember that each point on the unit circle...

Find the value of arcsin(x) for x = sqrt(3)/2 on the unit circle

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Find the value of $ arcsin(x) $ for $ x = sqrt{3}/2 $ on the unit circle Answer 1 Joseph Robinson To find the value of $ arcsin(x) $ for $ x = sqrt{3}/2 $ on the unit circle, we need to determine the angle $ theta $ such that $ sin(theta) = sqrt{3}/2 $ and $...

Find the sine and cosine values at different angles on the unit circle

by zhanhongyuan | Feb 4, 2025 | Unit Circle

Home Find the sine and cosine values at different angles on the unit circle Answer 1 Daniel Carter Given the unit circle, find the sine and cosine values for the following angles: 1. txt1 txt1 txt1$ radians 2. $frac{pi}{4}$ radians 3. $frac{pi}{2}$ radians 1. At txt1...