Find the sine and cosine of the angle θ on the unit circle when θ = 5π/4

by zhanhongyuan | Feb 1, 2025 | Unit Circle

Home Find the sine and cosine of the angle $ heta$ on the unit circle when $ heta = frac{5pi}{4}$ Answer 1 Maria Rodriguez To find the sine and cosine of the angle $theta = frac{5pi}{4}$ on the unit circle, we use the definitions of the trigonometric functions on the...

Find the coordinates of a point on the unit circle that corresponds to an angle of π/3 radians

by zhanhongyuan | Feb 1, 2025 | Unit Circle

Home Find the coordinates of a point on the unit circle that corresponds to an angle of $ frac{pi}{3} $ radians Answer 1 Emma Johnson To find the coordinates of a point on the unit circle corresponding to an angle of $ frac{pi}{3} $ radians:We can use the unit circle...

Find the angle θ in radians where cos(θ) = -1/2 and 0 ≤ θ < 2π

by zhanhongyuan | Feb 1, 2025 | Unit Circle

Home [et_pb_heading title=”Find the angle $ heta $ in radians where $ cos( heta) = -frac{1}{2} $ and $ 0 leq heta < 2pi $" _builder_version="4.27.3" _module_preset="default" title_font="--et_global_heading_font|500|||||||" title_text_color="#375375"...

Find the general solution of the equation tan(x) = cot(2x) on the unit circle

by zhanhongyuan | Feb 1, 2025 | Unit Circle

Home Find the general solution of the equation $ an(x) = cot(2x) $ on the unit circle Answer 1 Matthew Carter To solve the equation $ tan(x) = cot(2x) $ on the unit circle, we start by expressing $ cot(2x) $ in terms of $ tan(2x) $:$ cot(2x) = frac{1}{tan(2x)} $The...

Find the coordinates of the point on the unit circle corresponding to an angle of \( \frac{\pi}{4} \)

by zhanhongyuan | Feb 1, 2025 | Unit Circle

Home Find the coordinates of the point on the unit circle corresponding to an angle of $ frac{pi}{4} $ Answer 1 Amelia Mitchell To find the coordinates of the point on the unit circle corresponding to an angle of $ frac{pi}{4} $, we use the unit circle definition:The...

Determine the coordinates of a point on the unit circle at an angle of 11π/6

by zhanhongyuan | Feb 1, 2025 | Unit Circle

Home Determine the coordinates of a point on the unit circle at an angle of $ frac{11pi}{6} $ Answer 1 John Anderson To determine the coordinates of a point on the unit circle at an angle of $ frac{11pi}{6} $, we use the unit circle properties. The coordinates can be...

Solve for the exact values of all angles θ in the interval [0, 2π) that satisfy cos(θ) = -1/2

by zhanhongyuan | Feb 1, 2025 | Unit Circle

Home ”Solve Answer 1 Mia Harris To find the exact values of all angles $ theta $ in the interval $ [0, 2pi) $ that satisfy $ cos(theta) = -frac{1}{2} $, we use the unit circle. The cosine value of $ -frac{1}{2} $ corresponds to angles in the second and third...

Determine the coordinates of the point where the terminal side of an angle of 5π/3 radians intersects the unit circle, and identify its quadrant

by zhanhongyuan | Feb 1, 2025 | Unit Circle

Home Determine the coordinates of the point where the terminal side of an angle of $ frac{5pi}{3} $ radians intersects the unit circle, and identify its quadrant Answer 1 Samuel Scott The angle $ frac{5pi}{3} $ radians is equivalent to 300 degrees (since $...

Find the values of tan(x) at different positions on the unit circle

by zhanhongyuan | Feb 1, 2025 | Unit Circle

Home Find the values of $ an(x) $ at different positions on the unit circle Answer 1 William King To find the values of $ tan(x) $ at different positions on the unit circle, we use the definition:$ tan(x) = frac{ sin(x) }{ cos(x) } $First, let Answer 2 Amelia Mitchell...

Calculate the integral of 1/(x + sqrt(x^2 – 1)) over the interval [-1, 1]

by zhanhongyuan | Feb 1, 2025 | Unit Circle

Home ”Calculate Answer 1 Daniel Carter To calculate the integral: $ int_{-1}^{1} frac{1}{x + sqrt{x^2 – 1}} dx $ First, consider the substitution $ x = cosh(t) $, which implies $ dx = sinh(t) dt $. When $ x = -1 $, $ t = i pi $ and when $ x = 1 $, $ t = 0...