Question

If cot x =-12/5 , and π /2 < x < π , find sin (2x) Use

double-angle identities to answer the following questions

Answer 1

`-(120)/(169)`

Explanation:

cot = -12/5 meaning:

x : y = -12 : 5

(π /2 < x < π → Quadran 2 → x negative & y positive)

`r=√(x^2+y^2)`

`=√((-12)^2+5^2)`

`=13`

∴ x : y : r = -12 : 5 : 13

`sin\ x=(y)/(r)`

`=(5)/(13)`

`cos\ x=(x)/(r)`

`=(-12)/(13)`

`sin(2x)=2sin\ x\ cos\ x`

`=2*(5)/(13) *(-12)/(13)`

`=-(120)/(169)`