by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home [et_pb_heading title=”Find the exact value of $ an( heta) $ on the unit circle for the angle $ heta $ where $ 0 < heta < frac{pi}{2} $ and $ heta $ is the solution to the equation $ 2sin( heta)cos( heta) = 1 $." _builder_version="4.27.3"...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home What is the sine of $ frac{π}{6} $? Answer 1 Lucas Brown The sine of $ frac{π}{6} $ is found using the unit circle. At angle $ frac{π}{6} $, the y-coordinate of the corresponding point on the unit circle is: $ sin left( frac{π}{6} right) = frac{1}{2} $ Answer 2...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Evaluate the integral of $ frac{cos(2x)}{sqrt{1-sin^2(2x)}} $ with respect to $ x $ Answer 1 Henry Green To evaluate the integral $ int frac{cos(2x)}{sqrt{1-sin^2(2x)}} , dx $, we begin by recognizing that:$ sin^2(2x) + cos^2(2x) = 1 $Thus, the expression under...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Find the secant of an angle $ heta$ in a unit circle Answer 1 Benjamin Clark To find the secant of an angle $theta$ in a unit circle, we use the formula:$ sec(theta) = frac{1}{cos(theta)} $Suppose $theta$ is an angle in the first quadrant where cos(θ) = 0.6....
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Calculate the tangent of an angle when given the sine and cosine values in the unit circle Answer 1 Charlotte Davis To find the tangent of an angle in the unit circle when given the sine and cosine values, we use the formula:$ tan(theta) =...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Determine the values of $ cos( heta) $ and $ sin( heta) $ given that the point $ (x, y) $ is on the unit circle Answer 1 Matthew Carter Given that $ (x, y) $ is on the unit circle, we know:$ x^2 + y^2 = 1 $Using the definitions of the trigonometric functions on...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Define a unit circle and prove that any point $(x, y)$ on the unit circle satisfies the equation $x^2 + y^2 = 1$. Answer 1 Mia Harris A unit circle is a circle with a radius of 1 unit, centered at the origin (0,0) in the Cartesian coordinate system. To prove that...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Find the exact value of $ sin(frac{pi}{4}) $ on the unit circle. Answer 1 Alex Thompson To find the exact value of $ sin(frac{pi}{4}) $ on the unit circle, we recognize that $ frac{pi}{4} $ is equivalent to $ 45^{circ} $. On the unit circle, the coordinates for $...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Find the value of $ sin( heta) $ and $ cos( heta) $ where $ heta = frac{pi}{3} $ using the unit circle. Answer 1 John Anderson To find the values of $ sin(theta) $ and $ cos(theta) $ where $ theta = frac{pi}{3} $, we use the unit circle.On the unit circle, the...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Find the value of $ an(x) $ for $ x = frac{pi}{4} $ Answer 1 Alex Thompson To find the value of $ tan(x) $ when $ x = frac{pi}{4} $, we use the unit circle chart.For $ x = frac{pi}{4} $, the coordinates on the unit circle are (frac{sqrt{2}}{2},...