Question

Find sin 2x, cos 2x, and tan 2x if tan x= -3/2 and x terminates in quadrant IV.

Answer 1

Answer:

• sin 2x = -12/13

,

• cos 2x = -5/13

,

• tan 2x = 12/5

Step-by-step explanation:

Given that

`\tan x=-(3)/(2)`

Then

`\begin{gathered} \sin2x=(2\tan x)/(1+\tan^2x) \\ \\ =(2(-(3)/(2)))/(1+(-(3)/(2))^2)=(-3)/((13)/(4)) \\ \\ =-3*(4)/(13)=-(12)/(13) \end{gathered}`
`\begin{gathered} \cos2x=(1-\tan^2x)/(1+\tan^2x)=(1-(-(3)/(2))^2)/(1+(-(3)/(2))^2) \\ \\ =(1-(9)/(4))/(1+(9)/(4))=(-(5)/(4))/((13)/(4))=-(5)/(4)*(4)/(13)=-(5)/(13) \end{gathered}`
`\begin{gathered} \tan2x=(2\tan x)/(1-\tan^2x)=(2(-(3)/(2)))/(1-(-(3)/(2))^2) \\ \\ =(-3)/(1-(9)/(4))=(-3)/(-(5)/(4))=-3*(-4)/(5)=(12)/(5) \end{gathered}`