Mathematics: Convert the equation r cos theta = sin (2 theta) to Cartesian coordinates. Describe the resulting curves. Choose the correct equations below. A. x^2+ y^2 =1^2 and x = 0 B. (x - 1)^2 (y - 1)^ and x = 0 C. (x - 1)^2 + y^2 and x = 0 D. x^2 (y - 1)^2 = 1^2 and x = 0

Convert the equation r cos theta = sin (2 theta) - id25061299, rainbowprincess200

abalaam

18.01.2022

Correct option (D) x = 0 or x² + (y - 1)² = 1².

Step-by-step explanation:

The trigonometric equation is: $r\ Cos\ \theta=Sin\ 2\theta$

The expansion of $Sin\ 2\theta$ is:

$Sin\ 2\theta=2\ Sin\ \theta \ Cos\ \theta$

Then the equation is:

$r\ Cos\ \theta=Sin\ 2\theta\\r\ Cos\ \theta=2\ Sin\ \theta \ Cos\ \theta$

Now either $Cos\ \theta=0$ or $r=2Sin\ \theta$

In Cartesian form:

$x=Cos\ \theta\\y=Sin\ \theta$

Then either

x = 0

Or,

$\sqrt{x^{2}+y^{2}}=\frac{2y}{\sqrt{x^{2}+y^{2}}}\\x^{2}+y^{2}-2y=0\\x^{2}+y^{2}-2y+1=1\\x^{2}+(y-1)^{2}=1$

Thus, the resulting curve is: x = 0 or x² + (y - 1)² = 1².

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catwomn

20.12.2021

233,982

Step-by-step explanation:

222840x0.05=11142

222840+11,142= 233,982

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