Q:

Which angles are coterminal with 3pi/2?The answer choices are:11pi/2-pi/2Pi/2-7pi/2

Accepted Solution

A:
Answer:[tex]-\frac{\pi }{2}, \frac{11\pi }{2}[/tex]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: [tex]\frac{3\pi }{2}\pm k2\pi \leqslant 2\pi[/tex] 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 [tex]\frac{3\pi }{2}[/tex][tex]\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}[/tex] (...)From the given list, coterminal angles: [tex]-\frac{\pi }{2}[/tex] [tex]\frac{11\pi }{2}[/tex]