by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home Determine the $ an$ values of specific angles on the unit circle Answer 1 Lily Perez We need to determine the $tan$ values for the angles $30^{circ}$, $45^{circ}$, and $60^{circ}$ on the unit circle: 1. For $30^{circ}$: $tan 30^{circ} = frac{sin 30^{circ}}{cos...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home What are the sine, cosine, and tangent of the angle $frac{pi}{4}$ on the unit circle? Answer 1 Chloe Evans To find the sine, cosine, and tangent of the angle $frac{pi}{4}$ on the unit circle, we need to locate the angle on the circle. The angle $frac{pi}{4}$...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home Find the value of $csc(frac{pi}{3})$ using the unit circle Answer 1 John Anderson To find $csc(frac{pi}{3})$, we first need to recall the definition of the cosecant function: $csc(theta) = frac{1}{sin(theta)}$ Next, we locate the angle $frac{pi}{3}$ on the unit...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home Finding the Tangent of Angles on the Unit Circle Answer 1 Olivia Lee To find the tangent of an angle θ on the unit circle, we use the definition of tangent in terms of sine and cosine: $tan(theta) = frac{sin(theta)}{cos(theta)}$ Consider the angle θ = 45 degrees....
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home What are the sine and cosine values of an angle of $frac{pi}{6}$ on the unit circle? Answer 1 Amelia Mitchell The angle $frac{pi}{6}$ radians corresponds to 30 degrees. On the unit circle, the coordinates of the point at this angle represent the cosine and sine...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home Convert an angle from degrees to radians using the unit circle Answer 1 Samuel Scott The formula to convert degrees to radians is: ( theta = frac{pi}{180} times text{degrees} )Given an angle of 120 degrees, we use the following calculation:$ theta = frac{pi}{180}...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home Determine the exact values of $cot( heta)$ for an angle $ heta$ that, when doubled, corresponds to a point on the unit circle where the y-coordinate is equal to $-frac{sqrt{3}}{2}$. Answer 1 James Taylor To find $cot(theta)$, we need to determine the appropriate...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home Find the value of $ an left( frac{4pi}{3} ight) $ on the unit circle Answer 1 Isabella Walker To find $ tan left( frac{4pi}{3} right) $ on the unit circle, we note that $ frac{4pi}{3} $ radians is in the third quadrant.In the third quadrant, both sine and cosine...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home [et_pb_heading title=”If the unit circle in the complex plane is flipped upside down over the real axis, determine the new coordinates of the point $e^{i heta}$ where Define the unit circle in trigonometry leq heta < 2pi$." _builder_version="4.27.3"...
by zhanhongyuan | Feb 12, 2025 | Unit Circle
Home What is the cosine of the angle $45^circ$ on the unit circle? Answer 1 Chloe Evans The angle 45 degrees is equivalent to $frac{pi}{4}$ radians.On the unit circle, the coordinates for an angle of $45^circ$ or $frac{pi}{4}$ radians are $(frac{sqrt{2}}{2},...