Explain which trig functions and identities produce circles, ellipses and hyperbolas.

Step-by-step explanation:

The general equation for any conic section is:

Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0,

where A, B, C, D, E, F are fixed coefficients and A, B, C are not simultaneously equal to 0.

But, we can also write equations for conic section in terms of trigonometric functions using Parametric Equations:

For circle:

(x, y) = (rcos(theta), rsin(theta)) <=> x^2 + y^2 = r^2,

because  (cos(theta))^2 + (sin(theta))^2 = 1

For ellipse:

(x, y) = (acos(theta), bsin(theta)) or x^2/a^2 + y^2/b^2 = 1

because  (cos(theta))^2 + (sin(theta))^2 = 1

For hyperbola:

(x, y) = (asec(theta), btan(theta)) or  x^2/a^2 - y^2/b^2= 1

because  (cos(theta))^2 + (sin(theta))^2 = 1

whats the question?

step-by-step explanation: