How do you determine the quadrant in which $- 2$ $-2$ radians lies?

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Answer 1 · 2017-04-22T12:45:10

$- 2$ $-2$ radians lies in $Q 3$ $Q3$

We know that

$Q 1$ $Q1$ is from $0$ $0$ to $\frac{π}{2} = 1.5708$ $pi/2=1.5708$ radians

$Q 2$ $Q2$ is from $\frac{π}{2} = 1.5708$ $pi/2=1.5708$ to $π = 3.1416$ $pi=3.1416$ radians

$Q 3$ $Q3$ is from $π = 3.1416$ $pi=3.1416$ to $\frac{3 π}{2} = 4.7124$ $(3pi)/2=4.7124$ radians and

$Q 4$ $Q4$ is from $\frac{3 π}{2} = 4.7124$ $(3pi)/2=4.7124$ to $2 π = 6.2832$ $2pi=6.2832$ radians

Now $- 2$ $-2$ radians is equivalent to $- 2 + 2 π = - 2 + 6.2832 = 4.2832$ $-2+2pi=-2+6.2832=4.2832$ radians

Hence $- 2$ $-2$ radians lies in $Q 3$ $Q3$

How do you determine the quadrant in which −2-2 radians lies?