Question

Sandra wants to evaluate 2 cot(-9pi/2). Her work is shown below. what did she do wrong?

2 cot (-9pi/2) = 2 cot (9pi/2)
2 cot (-9pi/2) = 2 cot (pi/2)
2 cot (-9pi/2) = 2(0)
2 cot (-9pi/2) = 0


a)Since cot is an odd function 2 cot (-9pi/2) does not equal 2 cot(9pi/2)

b) since cot has a period of (pi) 2 cot(9pi/2) does not equal 2 cot (pi/2)

c) since cot evaluated at pi/2 is not 0, 2 cot(pi/2) does not equal 2(0)

d) since cot cannot be multiplied by a factor 2(0) does not equal 0

Answer 1

Option A - Since cot is an odd function
`2 cot(-(9\pi)/(2))` does not equal
`2 cot((9\pi)/(2))`

Step-by-step explanation:

Given : Sandra wants to evaluate
`2 cot(-(9\pi)/(2))`

To find : What did she do wrong?

Solution : In the first step she took a wrong step because cot is an odd function so
`cot(-x)= -cot x`

The exact steps are :

`2cot(-(9\pi)/(2))=-2cot ((9\pi)/(2))`

`2cot(-(9\pi)/(2))=-2cot ((\pi)/(2))`

`2cot(-(9\pi)/(2))=-2(0)`

`2cot(-(9\pi)/(2))=0`

Therefore, option A is correct .