Rectangular and polar forms are two forms of equations that translates to plot. In this case, the two forms are convertible to each other by the expressions:

r sin theta = y
r cos theta = x
x2 + y2 = r2

we are given the polar expression r csc theta = 8 and is asked to convert to rectangular form.

in this case, csc theta is equal to 1/ sin theta. thys
r / sin theta = 8

in order to make use of the equations above, then

we multiply r to both numerator and denominator in the left side, that is
r^2 / r sin theta = 8
x2+y2 / y = 8
x 2 + y2 = 8y

3 0

3 years ago

Which is equivalent to √3/√8 when denominator is "rationalized"?

TEA [102]

Step-by-step explanation:

$\dfrac{\sqrt3}{\sqrt8}=\dfrac{\sqrt3\cdot\sqrt2}{\sqrt8\cdot\sqrt2}=\dfrac{\sqrt{3\cdot2}}{\sqrt{8\cdot2}}=\dfrac{\sqrt6}{\sqrt{16}}=\dfrac{\sqrt6}{4}$

$\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\\sqrt{a}=b\iff b^2=a\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\\sqrt{16}=4\ \text{because}\ 4^2=16$

4 0

3 years ago