Question

If tan(x) = -1/3, cos(x) >0, then what is sin(2x), cos(2x), and tan(2x)?

Answer 1

x must be in the fourth quadrant where tan(x) is negative and cos(x) is positive.

Find the hypotenuse in the diagram shown above.
Then find sin(x), cos(x). sin(x) should be negative and cos(x) should be positive.

sin(2x) = 2sin(x)cos(x). Substitute and find sin(2x).

Answer 2

cos(2x) = 2cos^2(x) - 1
tan(2x) = sin(2x) / cos(2x)

Answer 3

this is your triangle in the fourth quadrant

Answer 4

like @aum said find the hypotenuse first then
find sinx conx tanx
and use them for double angles

Answer 5

and so the hypotenuse would be sqrt(3^2+1^2) , which gives about 3.16

Answer 6

yes! but you don't need decimal
\(\sqrt{10}\) leave it this way

Answer 7

so sin(x) = -1/sqrt(10) , cos(x) = 3/sqrt(10) , tan(x) = -1/3. right?

Answer 8

Correct.

Answer 9

sin(2x) = 2sin(x)cos(x) = 2 * (-1 / sqrt(10) ) * (3 / sqrt(10)) = ?

Answer 10

that would be -3/5

Answer 11

Yes.

Answer 12

cos(2x) would be 4/5

Answer 13

correct.

Answer 14

and tan(2x) would be -3/4

Answer 15

Got it.

Answer 16

Thank you so much!

Answer 17

You are welcome.