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Determine two pairs of polar coordinates for the point (5, -5) with 0° ≤ θ < 360°.

2 Answers

3 votes

Answer:

Explanation:

(5 rad 2, 135 degrees),(-5 rad 2, 315 degrees)

User Namig Hajiyev
by
7.4k points
2 votes

\bf \begin{array}{llll} 5&amp;,&amp;-5\\ x&amp;&amp;y \end{array}\qquad \begin{cases} r=√(x^2+y^2)\\\\ \theta=tan^(-1)\left( (y)/(x) \right) \end{cases}\\\\ -----------------------------\\\\ r=√((5)^2+(-5)^2)\implies r√(50)\implies \boxed{r=5√(2)} \\\\\\ \theta=tan^(-1)\left( (-5)/(5) \right)\implies 0=tan^(-1)(-1)

now.... the tangent is -1 when the "y" and "x" are of different signs
now, that happens in the 2nd and 4th quadrant, however, let's take a look at our terminal point, 5 , -5

the "x" is positive, the "y" is negative, that means, is the one on the 4th quadrant
\bf \theta=(7\pi )/(4)

thus
\bf \left( 5√(2)\ ,\ (7\pi )/(4) \right)
User Gabriele Mariotti
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6.6k points