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

Which angles are coterminal with 3pi/2? the answer

Ответ:

lejeanjamespete1

16.03.2022

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

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 $\frac{3\pi }{2}$

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