January 21, 2024

Interactive Unit Circle - Trigonometry

This interactive animation shows the variation of essential trigonometric functions with changes in angle, it also has a graph that syncs perfectly with the unit circle animation.

(1,0)

(\frac{\sqrt{3}}{2}, \frac{1}{2})

(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}})

(\frac{1}{2}, \frac{\sqrt{3}}{2})

(0,1)

(- \frac{1}{2}, \frac{\sqrt{3}}{2})

(- \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}})

(- \frac{\sqrt{3}}{2}, \frac{1}{2})

(- 1,0)

(- \frac{\sqrt{3}}{2}, - \frac{1}{2})

(- \frac{1}{\sqrt{2}}, - \frac{1}{\sqrt{2}})

(- \frac{1}{2}, - \frac{\sqrt{3}}{2})

(0, - 1)

(\frac{1}{2}, - \frac{\sqrt{3}}{2})

(\frac{1}{\sqrt{2}}, - \frac{1}{\sqrt{2}})

(\frac{\sqrt{3}}{2}, - \frac{1}{2})

Sine (sin): The sine function represents the ratio of the length of the side opposite of the angle to the length of the hypotenuse in a right triangle. It is particularly useful in modeling periodic phenomena like sound waves and oscillations.
Cosine (cos): Cosine is also a ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. It’s also used to describe cyclical processes and phenomena.
Tangent (tan): The tangent function is the ratio of the sine to the cosine. It describes the slope of a line.
Secant (sec), Cosecant (csc), and Cotangent (cot) are the reciprocal functions of sine, cosine, and tangent, respectively. They are defined as sec(x) = 1/cos(x), csc(x) = 1/sin(x), and cot(x) = 1/tan(x).

# trigonometry # animations # interactive