What is the value of sin(15 degrees) using the unit circle?

by zhanhongyuan | Feb 6, 2025 | Unit Circle

Home What is the value of $ sin(15^circ) $ using the unit circle? Answer 1 Chloe Evans To find the value of $ sin(15^circ) $ using the unit circle, we use the angle addition formula:$ sin(a + b) = sin(a) cos(b) + cos(a)sin(b) $Here, let $ a = 45^circ $ and $ b =...

Solve for the trigonometric value of tan(x) when cos(x) = 1/2 on the unit circle

by zhanhongyuan | Feb 6, 2025 | Unit Circle

Home Solve for the trigonometric value of $ an(x) $ when $ cos(x) = frac{1}{2} $ on the unit circle Answer 1 Christopher Garcia To solve for $ tan(x) $ given $ cos(x) = frac{1}{2} $ on the unit circle, we must first determine the corresponding $ sin(x) $. On the unit...

Find the coordinates of the point on the unit circle that corresponds to an angle of pi/3

by zhanhongyuan | Feb 6, 2025 | Unit Circle

Home Find the coordinates of the point on the unit circle that corresponds to an angle of $ pi/3 $ Answer 1 Abigail Nelson To find the coordinates of the point on the unit circle at an angle of $ pi/3 $ , we use the fact that the unit circle Answer 2 Ava Martin The...

Complete the unit circle with the correct trigonometric values

by zhanhongyuan | Feb 6, 2025 | Unit Circle

Home Complete the unit circle with the correct trigonometric values. Answer 1 Matthew Carter To complete the unit circle, fill in the following values:$text{1. } sin(frac{pi}{6}) = frac{1}{2}, cos(frac{pi}{6}) = frac{sqrt{3}}{2}$$text{2. } sin(frac{pi}{4}) =...

Find the coordinates on the unit circle at an angle of π/3

by zhanhongyuan | Feb 6, 2025 | Unit Circle

Home Find the coordinates on the unit circle at an angle of $ frac{pi}{3} $ Answer 1 Christopher Garcia To find the coordinates on the unit circle at an angle of $ frac{pi}{3} $, we use the unit circle definition: $ (cos(theta), sin(theta)) $For $ theta = frac{pi}{3}...

Determine the values of theta that satisfy both sin(theta) = -1/2 and cos(theta) = -sqrt(3)/2

by zhanhongyuan | Feb 6, 2025 | Unit Circle

Home Determine the values of $ heta $ that satisfy both $ sin( heta) = -frac{1}{2} $ and $ cos( heta) = -frac{sqrt{3}}{2} $ Answer 1 Ava Martin First, recognize that $ sin(theta) = -frac{1}{2} $ in the third and fourth quadrants. The angles in these quadrants are $...

Find the hypotenuse of a right triangle on the unit circle with one side equal to 1/√2

by zhanhongyuan | Feb 6, 2025 | Unit Circle

Home Find the hypotenuse of a right triangle on the unit circle with one side equal to $ frac{1}{sqrt{2}} $ Answer 1 Amelia Mitchell In a right triangle on the unit circle, the hypotenuse is always 1. If one side is $ frac{1}{sqrt{2}} $, the other side must also be $...

Determine the value of sin, cos, and tan for the angle θ = π/4 using the unit circle

by zhanhongyuan | Feb 5, 2025 | Unit Circle

Home Determine the value of $sin$, $cos$, and $ an$ for the angle $ heta = frac{pi}{4}$ using the unit circle Answer 1 Daniel Carter Given the angle $theta = frac{pi}{4}$, the corresponding coordinates on the unit circle are:$ (cos(theta), sin(theta)) =...

Find the coordinates of the point on the unit circle where the angle is 3π/4 radians

by zhanhongyuan | Feb 5, 2025 | Unit Circle

Home Find the coordinates of the point on the unit circle where the angle is $frac{3pi}{4}$ radians. Answer 1 Emma Johnson To find the coordinates of the point on the unit circle where the angle is $frac{3pi}{4}$ radians, we use the unit circle definition:The...

Determine the exact values of the trigonometric functions for angle 7π/6

by zhanhongyuan | Feb 5, 2025 | Unit Circle

Home Determine the exact values of the trigonometric functions for angle $ frac{7pi}{6} $ Answer 1 Olivia Lee To determine the exact values of the trigonometric functions for angle $ frac{7pi}{6} $, we follow these steps:1. Recognize that $ frac{7pi}{6} $ is in the...