Help me i really don't understand

Mathematics

1 answer:

finlep [7]3 years ago

4 0

1) 1 dot
2) figure 1 + 3 dots
3) figure 2 + 5 dots
4) figure 3 + 7 dots
5) figure 4 + 9 dots
and keeps going....

The next figure, takes the solution of last figure and add odd number in increasing order.
In this type of problem, find a matter.

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$A)(5,\frac{3\pi}{2})=(0,-5)\:B)(\frac{3}{2} , \frac{\pi}{4} ) \Rightarrow (\frac{3\sqrt{2}}{4} ,\frac{3\sqrt{2}}{4} )\:C)(-1,\frac{\pi}{6})= (\frac{\sqrt{3}}{2},\frac{1}{2})$

Step-by-step explanation:

1) Check the Polar Coordinates on the graph.

2) A polar coordinate is given in $(r,\theta)$ Let's transform each polar coordinate into Cartesian one. Considering:

$x=rcos\theta\\y=rsin\theta\\$

$A) (5,\frac{3\pi}{2})\\cos(\theta)=\frac{x}{5}\\cos(\frac{3\pi}{2})=\frac{x}{5}\:Cross\: Multiplying\\x=5 cos(\frac{3\pi}{2})\\x =5 cos(0)\:x=0\\sin(\frac{3\pi}{2})=\frac{y}{5}\\y=5sin(-1)\\y=-5\\(0,-5)$

B) (b) (3/2 , π/4)

$B) (\frac{3}{2},\frac{\pi}{4})\\cos(\theta)=\frac{x}{\frac{3}{2}}\\\frac{3}{2}cos(\frac{\pi}{4})=x\:Cross\: Multiplying\\x=\frac{3}{2}*\frac{\sqrt{2}}{2}\\x =\frac{3\sqrt{2}}{4} \approx 1.06$