by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home $ ext{Find the angle } heta ext{ in the unit circle where } cos( heta) = 0.5$ Answer 1 Ava Martin $text{Given } cos(theta) = 0.5$$text{We know that } cos(theta) = 0.5 text{ at } theta = frac{pi}{3} text{ and } theta = -frac{pi}{3} text{ (or equivalently } theta =...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Find the exact values of $sin( heta)$ and $cos( heta)$ using the unit circle. Answer 1 Emma Johnson To find the exact values of $sin(theta)$ and $cos(theta)$ using the unit circle, let’s consider $theta = frac{5pi}{6}$.First, we know that $frac{5pi}{6}$ is...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Determine the expression for the flipped unit circle equation Answer 1 Charlotte Davis To determine the equation for a unit circle flipped over the y-axis, we start with the standard unit circle equation: $x^2 + y^2 = 1$ When we flip the unit circle over the...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Find the value of $cos heta$ on the unit circle in the complex plane when $ heta = pi/3$. Answer 1 Mia Harris To find the value of $cos theta$ on the unit circle, we use the unit circle definition where the coordinates are $(cos theta, sin theta)$. For $theta =...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home ”$ Answer 1 William King To solve for all angles ( theta ) in the interval ([0, 2pi)) where ( cos(theta + pi/6) = sqrt{3}/2 ), we first identify the standard angles where cosine equals ( sqrt{3}/2 ). These angles are: $alpha = 0 text{ or } alpha = 2pi$...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Find the exact values of sine, cosine, and tangent for the angle $ heta $ where $ heta $ is in the third quadrant, and the terminal side of $ heta $ passes through the point $ (-3, -4) $ on the unit circle. Answer 1 Emma Johnson Given point $(-3, -4)$, we first...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Calculate the trigonometric values at specific angles on the unit circle Answer 1 Emily Hall Given the angle $ theta = frac{3pi}{4} $, find the values of $ sin theta $, $ cos theta $, and $ tan theta $. Step 1: Identify the reference angle. The reference angle...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home For a unit circle centered at the origin, consider a point $P$ on the circle described by the angle $ heta$ measured from the positive x-axis in the counterclockwise direction. Determine the coordinates of the point $Q$, which is the reflection of $P$ ac Answer 1...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Finding Trigonometric Values at Specific Angles on the Unit Circle Answer 1 Lucas Brown To find the trigonometric values of an angle of 150 degrees on the unit circle, we can use the angle relationship and symmetry of the unit circle. 1. Convert the angle to...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Find the secant of an angle on the unit circle for $ heta = 45^{circ}$. Answer 1 Lucas Brown To find the secant of the angle $theta = 45^{circ}$ on the unit circle, we use the relationship between secant and cosine.The secant of an angle is the reciprocal of its...