How do you determine the quadrant in which $3.5$ $3.5$ radians lies?

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How do you determine the quadrant in which $3.5$ $3.5$ radians lies?

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Answer 1 · 2018-06-14T19:25:02

$3.5$ $3.5$ radians lies in quadrant III.

Explanation:

Since we know the measure in degrees of multiples of $\frac{π}{2}$ $pi/2$ radians, it would be nice to create an inequality that contains $3.5$ $3.5$ radians. We will use the approximation $π \approx 3.14$ $pi~~3.14$ and from that it follows that $\frac{π}{2} \approx 1.57$ $pi/2~~1.57$ . Since $3.14 < 3.5 < 3.14 + 1.57$ $3.14<3.5<3.14+1.57$ , we can write this inequality like this: $π < 3.5 < \frac{3 π}{2}$ $pi<3.5<(3pi)/2$ . Since we know that $π$ $pi$ radians is equal to $180^{o}$ $180^o$ and $\frac{3 π}{2}$ $(3pi)/2$ radians is equal to $270^{o}$ $270^o$ , 3.5 radians lies in the third quadrant.

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How do you determine the quadrant in which $3.5$ $3.5$ radians lies?

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