Question

An angle in standard position measures 7π4 radians.

In which quadrant does the terminal side of this angle lie?




Quadrant I

Quadrant II

Quadrant III

Quadrant IV

Answer 1

For a second opinion, it is indeed Quadrant IV :)

Answer 2

$7\pi /4$  lies in Quadrant IV

Let us assume an angle $\alpha$. if,

$0<\alpha <\pi /2$  it lies in quadrant I

$\pi /2<\alpha <\pi$  it lies in quadrant II

$\pi <\alpha <3\pi /2$  it lies in quadrant III

$3\pi /2<\alpha <2\pi$ it lies in quadrant IV

Now, $7\pi /4 = 3\pi /2+\pi /4$

         $7\pi /4 = 2\pi -\pi /4$  also

which means $3\pi /2<\ 7\pi/4 <2\pi$

So, $7\pi /4$  lies in Quadrant IV

Learn more about Quadrants:

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