How do you convert $r = 2 sin r + 2 cos r$ $r= 2 sin r + 2 cos r$ into cartesian form?

Question

How do you convert $r = 2 sin r + 2 cos r$ $r= 2 sin r + 2 cos r$ into cartesian form?

1 Answer

Impact of this question

9060 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-28T05:09:50

Perhaps, the equation is $r = 2 (sin θ + cos θ)$ $r=2(sin theta + cos theta)$ . If so, the cartesian form is ${(x - 1)}^{2} + {(y - 1)}^{2} = 2$ $(x-1)^2+(y-1)^2=2$ .

Explanation:

I solve this for the corrected version $r = 2 (sin θ + cos θ)$ $r = 2 (sin theta + cos theta )$

The conversion equation is $r) cos θ, sin θ) = (x, y)$ $r)cos theta, sin theta ) = (x, y)$ that

gives ) $r = \sqrt{x^{2} + y^{2}} \geq 0$ $r= sqrt(x^2+y^2)>=0$ , for the principal value,

$sin θ = \frac{y}{\sqrt{x^{2} + y^{2}}} and cos θ = \frac{x}{\sqrt{x^{2} + y^{2}}}$ $sin theta = y/sqrt(x^2+y^2) and cos theta = x/sqrt(x^2+y^2)$

Here,

$\sqrt{x^{2} + y^{2}} = 2 \frac{x + y}{\sqrt{x^{2} + y^{2}}}$ $sqrt(x^2+y^2)= 2(x + y)/sqrt(x^2+y^2)$ ,

Cross multiplying and reorganizing,

${(x - 1)}^{2} + {(y - 1)}^{2} = 2$ $(x-1)^2+(y-1)^2=2$

Science

Math

Humanities

... and beyond

How do you convert $r = 2 sin r + 2 cos r$ $r= 2 sin r + 2 cos r$ into cartesian form?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you convert r= 2 sin r + 2 cos rr=2sinr+2cosrr= 2 sin r + 2 cos r into cartesian form?

1 Answer

Explanation:

Related questions

Impact of this question

How do you convert $r = 2 sin r + 2 cos r$ $r= 2 sin r + 2 cos r$ into cartesian form?