Question

Which value is the solution for the equation cotx/2=-1?

A. 3pi/2
B. 3pi/4
C. 5pi/4
D. 7pi/4

Answer 1

cot(x/2) or cot(x)/2?

Answer 2

The first one

Answer 3

First solve \[x/2=cot^{-1}(-1)\].
Then you have a normal equation for which you can solve x.
Don't forget that there are multiple possible answers for arccot. It's of the form (...+k*pi with k element of Z)

Answer 4

$$
\bf \large {
cot\pmatrix{\frac{x}{2}} = -1\\
cot^{-1}\pmatrix{cot\pmatrix{\frac{x}{2}}} = cot^{-1}(-1)\\
\frac{x}{2} = \frac{3 \pi}{4}, \frac{7 \pi}{4}\\
}
$$

Answer 5

or you can plug in choices one by one and see which one satisfies your equation...

Answer 6

Nvm totally wrong :p

Answer 7

I can only pick one....

Answer 8

lets try 1st one,
cot (x/2) = cot (3pi/4) = ... ?

Answer 9

$$
\frac{x}{2} = \frac{3 \pi}{4}, \frac{7 \pi}{4}\\
\frac{x}{2} = \frac{3 \pi}{4} \implies x = \frac{3 \pi}{2}\\
\frac{x}{2}=\frac{7 \pi}{4} \implies x = \frac{14 \pi}{4}
$$

Answer 10

I think its A

Answer 11

correct :)
because cot (3pi/4) = -1 ...

Answer 12

yes, the other choice will be \(\cfrac{7\pi}{2}\) and is not in the choices

Answer 13

A is correct!