Help me with this Maths problem pls? ASAP?

Question

Find the cartesian equation for the curve.
x=-1+sinθ , y=2+cosθ, 0≤θ≤2π.

Answer 1

In what follows I'll use t instead of theta.

(x+1)=sin t, (y-2)=cos t --> (x+1)^2+(y-2)^2 = sin^2 t+ cos^2 t = 1 --> (x+1)^2+(y-2)^2=1.

It is a circle with radius 1 and center (-1, 2). Nice and tidy.

Answer 2

This is a parametric equation with theta as the parameter. Solve for theta from the x equation:

theta = arcsin(x - 1)

then substitute into the y equation:

y = 2 + cos[arcsin(x - 1)].

In general, cos[arcsin(a)] = ±√[1 - a^2], 0 ≤ arcsin(a) ≤ 2π

Using this relation

y = 2 ± √[1 - (1 - x)^2]

y = 2 ± √[-x^2 + 2x]

(y+2)^2 = 2x - x^2 --> y^2 + x^2 +2y - 2x + 4 = 0

This is some type of conic section.

Answer 3

From Wikipedia:

In mathematics, the Cartesian coordinate system is used to determine each point uniquely in a plane through two numbers, usually called the x-coordinate and the y-coordinate of the point. To define the coordinates, two perpendicular directed lines (the x-axis or abscissa and the y-axis or ordinate), are specified, as well as the unit length, which is marked off on the two axes (see Figure 1). Cartesian coordinate systems are also used in space (where three coordinates are used) and in higher dimensions.

Using the Cartesian coordinate system geometric shapes (such as curves) can be described by algebraic equations, namely equations satisfied by the coordinates of the points lying on the shape. For example, the circle of radius 2 may be described by the equation x² + y² = 4 (see Figure 2).

Cartesian means relating to the French mathematician and philosopher René Descartes (Latin: Cartesius), who, among other things, worked to merge algebra and Euclidean geometry. This work was influential in the development of analytic geometry, calculus, and cartography.

The idea of this system was developed in 1637 in two writings by Descartes. In part two of his Discourse on Method Descartes introduces the new idea of specifying the position of a point or object on a surface, using two intersecting axes as measuring guides. In La Géométrie, he further explores the above-mentioned concepts.

See coordinates (mathematics) for other commonly used coordinate systems such as polar coordinates and coordinate systems for usage of the term in advanced mathematics.

Good Luck....

Answer 4

Pipe no individual million on my own = 2 hours or one hundred twenty minutes Pipe no 2 on my own = 3 hours or one hundred and eighty minutes Pipe no 3 on my own = a million hour or 60 minutes So at the same time in a million minute they fill a million/one hundred twenty + a million/one hundred and eighty + a million/60 = 3/360 + 2/360 + 6/360 = 11/360 of the tank So at the same time they are going to fill the tank in 360/11 = 32.seventy 3 minutes answer