Question

Which angles are coterminal with 3pi/2?

Answer 1

Answer:

$-\frac{\pi }{2}, \frac{11\pi }{2}$

Step-by-step explanation:

Coterminal angles are angles with the same initial and terminal side. In this question, the unit is Radians. They can be found algebraically by this formula for 3π/2:

$\frac{3\pi }{2}\pm k2\pi \leqslant 2\pi$ where K is an integer number for the number of "laps" around the origin (360º or 2π rad),  with a positive or negative direction .

So let's check some coterminal angles with $\frac{3\pi }{2}$

$\frac{3\pi }{2}-2\pi =-\frac{\pi }{2}\\\Rightarrow \frac{3\pi }{2}+2\pi =\frac{7\pi }{2}\\\frac{3\pi }{2}+2*2\pi =\frac{11\pi }{2}\\\Rightarrow \frac{3\pi }{2}-2*2\pi =\frac{5\pi }{2}\\\frac{3\pi }{2}-3*2\pi=-\frac{9\pi }{2}\\\Rightarrow \frac{3\pi }{2}+3*2\pi=-\frac{15\pi }{2}$

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From the given list, coterminal angles:

$-\frac{\pi }{2}$

$\frac{11\pi }{2}$

Answer 2

Your two answers are going to be-

π/2

&

-π/2