Question

Which value is a solution for the equation

Answer 1

\[\cot \frac{ x }{ 2 } =0\]

Answer 2

cot A = cos A /sin A
cot (x/2) = 0 will give you
cos (x/2) / sin (x/2) = 0 ----> cos (x/2) = 0
see the unit circle and tell when is cos value = 0 ?

Answer 3

pi/2 and 3pi/2 ???

Answer 4

yes,
so, x/2 = those,
so, x=... ?

Answer 5

what?

Answer 6

you got ,
x/2 = pi/2 and x/2 = 3pi/2
these are correct, now find x

Answer 7

oh ok

Answer 8

you need general form or in the range 0,2pi ?

Answer 9

well the 1st one i got pi

Answer 10

is correct

Answer 11

ok
now what

Answer 12

you need general form or in the range 0,2pi ?

Answer 13

whats that?

Answer 14

does your question say to write general form ? (if you have choices, list them)

Answer 15

Think about it. what is cot(x)?

cot (x) = cos(x)/sin(x)

Lets take 90 degrees. cos(x)/sin(x) = 0/1 = 0

270 degrees, cos(x)/sin(x) = 0/-1 = 0

So every pi/2 radians, you will get a 0.

x/2 = pi/2

2x= 2 pi

x = pi

Now we know we're going to add a +pi for every full rotation.

In finding the general form for cot(x/2)= 0 from [0,2pi] , we state that that

2*pi*n +pi will give us 0 for every full rotation from 0 to 2pi.

n = 0

2 * pi *(0) + pi = pi, we start there.

n = 1

2 * pi * (1) + pi = 3 pi.

etc..

Answer 16

3pi/4
3pi/2
pi/2
3pi

Answer 17

i chose 3pi

Answer 18

and that is correct :)
x/2 = 3pi/2
x = 3pi

Answer 19

yay!