Answer:
The location of the fly in polar coordinates is [tex](2.28,37.87\°)[/tex]
Step-by-step explanation:
we know that
The Cartesian coordinates of the fly are (1.8,1.4)
Convert Cartesian coordinates to Polar coordinates
[tex](x,y) ------> (r,\theta)[/tex]
Step 1
Find the value of r
Use Pythagoras Theorem to find the long side (the hypotenuse) r
[tex]r^{2}=x^{2}+y^{2}[/tex]
substitute
[tex]r^{2}=1.8^{2}+1.4^{2}[/tex]
[tex]r^{2}=5.2[/tex]
[tex]r=2.28[/tex]
Step 2
Find the angle theta
Use the Tangent Function to find the angle [tex]\theta[/tex]
[tex]tan(\theta)=\frac{y}{x}[/tex]
substitute
[tex]tan(\theta)=\frac{1.4}{1.8}[/tex]
[tex]\theta=arctan(\frac{1.4}{1.8})[/tex]
[tex]\theta=37.87\°[/tex]
therefore
The location of the fly in polar coordinates is [tex](2.28,37.87\°)[/tex]
