by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Given that ( heta ) is an angle in the unit circle such that its terminal side passes through the point ((a,b)). If the line passing through ((a,b)) and the origin makes an angle ( alpha ) with the x-axis, find the values of ( sin(alpha) ), Answer 1 Matthew...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home $ ext{Find the sine and cosine of a 45-degree angle}$ Answer 1 Alex Thompson To find the sine and cosine of a 45-degree angle, we can use the unit circle. A 45-degree angle corresponds to $frac{pi}{4}$ radians.On the unit circle, the coordinates for $frac{pi}{4}$...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home What are the coordinates of the point on the unit circle where the angle is $frac{pi}{3}$? Answer 1 Henry Green To find the coordinates of the point on the unit circle at an angle of $frac{pi}{3}$ radians, we use the trigonometric functions cosine and sine.For an...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Find the value of $ tan(frac{pi}{4}) $ using the unit circle. Answer 1 Ava Martin To find the value of $ tan(frac{pi}{4}) $ using the unit circle, we need to consider the coordinates of the point on the unit circle at the angle $ frac{pi}{4} $. The coordinates of...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Find the trigonometric values for an angle in the unit circle Answer 1 Henry Green Given an angle ( theta = frac{5pi}{4} ), find the values of ( sin(theta) ), ( cos(theta) ), and ( tan(theta) ). First, determine the reference angle in the unit circle. ( theta =...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Determining the Position of $-pi/2$ on the Unit Circle Answer 1 Abigail Nelson To locate the position of $-pi/2$ on the unit circle, we need to understand the unit circle itself. The circle has a radius of 1 and is centered at the origin (0,0).1. Start from the...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Determine the Value of $sec( heta)$ Given the Coordinates on the Unit Circle Answer 1 Lucas Brown Given a point on the unit circle with coordinates (0.6, 0.8), determine the value of $sec(theta)$. Step 1: Recall the definition of the point on the unit circle:...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Find the sine and cosine of the angle where the terminal side intersects the unit circle at the point $ left( -frac{1}{2}, frac{sqrt{3}}{2} ight) $. Answer 1 Chloe Evans To find the sine and cosine of the angle whose terminal side intersects the unit circle at...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home Find the angle in the unit circle Answer 1 Emma Johnson Given a point on the unit circle, find the angle such that $sin(theta) = frac{sqrt{3}}{2}$ and $cos(theta) = frac{1}{2}$.First, recognize that the coordinates given correspond to the point $(frac{1}{2},...
by zhanhongyuan | Feb 16, 2025 | Unit Circle
Home What is the tangent of 45 degrees on the unit circle? Answer 1 Mia Harris The tangent of an angle in the unit circle is given by $ tan(theta) = frac{sin(theta)}{cos(theta)} $. For $ theta = 45^{circ} $ or $ theta = frac{pi}{4} $ rad: $ sin(45^{circ}) =...