Question

Convert the polar coordinates to rectangular form (√2,-π\4)

Answer 1

Answer:

(1, -1)

Step-by-step explanation:

To convert polar to rectangular coordinates, use these identities:

• x = rcos(Ф)
• y = rsin(Ф)
• x² + y² = r²  

Here we were given the point $(\sqrt{2},-\frac{\pi}{4})$ which is our (r, Ф) point

We can now plug these values into our x and y equations to convert to rectangular and find our (x, y) point

• x = $(\sqrt{2} )cos(-\frac{\pi}{4} )= (\sqrt{2})(\frac{\sqrt{2} }{2})=\frac{2}{2}=1$
• y = $(\sqrt{2} )sin(-\frac{\pi}{4} )= (\sqrt{2})(-\frac{\sqrt{2} }{2})=-\frac{2}{2}=-1$

So our (x, y) point is (1, -1)

• $(\sqrt{2},-\frac{\pi}{4}) = (1, -1)$