by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the sine and cosine of $45^circ$ and $135^circ$ using the unit circle. Answer 1 Sophia Williams Using the unit circle, we know that:$45^circ = frac{pi}{4}$and$135^circ = frac{3pi}{4}$For $45^circ$:$sin 45^circ = sin frac{pi}{4} = frac{sqrt{2}}{2}$$cos...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home $ ext{Find the tangent values for specific angles on the unit circle}$ Answer 1 Mia Harris To find the tangent values for specific angles on the unit circle, we can use the fact that $tan(theta) = frac{sin(theta)}{cos(theta)}$.Let’s find the tangent value...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the value of $cot( heta)$ given that $ heta$ is a point on the unit circle where $cos( heta) = a$ and $sin( heta) = b$. Answer 1 Lucas Brown Since $cot(theta) = frac{cos(theta)}{sin(theta)}$, we can use the given values of $cos(theta)$ and $sin(theta)$.Given...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home $ ext{Find the value of tangent for given angles on the unit circle}$ Answer 1 John Anderson Given the angle $theta = frac{pi}{4}$, we need to find the value of $tan(theta)$.On the unit circle, the coordinates for $theta = frac{pi}{4}$ are $(frac{sqrt{2}}{2},...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Compute $ an left( frac{4pi}{3} ight)$ using the unit circle Answer 1 Chloe Evans To find $tan left( frac{4pi}{3} right)$, we use the unit circle. The angle $frac{4pi}{3}$ is in the third quadrant where tangent is positive since both sine and cosine are negative...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the values of $cot heta$ on the unit circle Answer 1 Daniel Carter The cotangent function is defined as the ratio of the cosine of an angle to the sine of the angle: $cot theta = frac{cos theta}{sin theta}$Given that the angle $theta$ is located at...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Calculate the points of intersection of the unit circle and the line passing through the origin with a given slope $ m $ Answer 1 Amelia Mitchell To find the points of intersection of the unit circle $x^2 + y^2 = 1$ and the line passing through the origin with...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home What is the value of $sin(frac{pi}{6})$ and $cos(frac{pi}{6})$ on the unit circle? Answer 1 Lily Perez To find the values of $sin(frac{pi}{6})$ and $cos(frac{pi}{6})$ on the unit circle, we need to understand the coordinates of the point on the unit circle...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the exact value of $ an( heta)$ given the point on the unit circle Answer 1 Matthew Carter Given a point on the unit circle at $(-frac{1}{2}, -frac{sqrt{3}}{2})$, find the exact value of $tan(theta)$.First, identify the coordinates $x$ and $y$ from the...
by zhanhongyuan | Feb 15, 2025 | Unit Circle
Home Find the coordinates on the unit circle for the angle corresponding to $-frac{2}{3}pi$ radians Answer 1 Chloe Evans To find the coordinates on the unit circle for the angle corresponding to $-frac{2}{3}pi$ radians, we first determine the reference angle. The...