find exact value

[magmagod]

if sin(x) = (-4/5), then find the exact value of the following:

a. tan(x)
b. sin(2x)

this is what i did to b.

2 sinx cosx
2 (-4/5)(3/5)
2(-12/25)
-24/25

i got cos x by the pyth theorm (x^2+y^2=r^2)

im really confused cause it says it might have two answers and what not..so please help

[MAS1]

Originally Posted by magmagod

if sin(x) = (-4/5), then find the exact value of the following:

a. tan(x)
b. sin(2x)

this is what i did to b.

2 sinx cosx
2 (-4/5)(3/5)
2(-12/25)
-24/25

i got cos x by the pyth theorm (x^2+y^2=r^2)

im really confused cause it says it might have two answers and what not..so please help

Since sin(x) = -4/5 draw two right triangles on a xy plane, one triangle in quadrant III and one in quadrant IV. Both triangles have a hypotenuse of 5, a leg of 4 in the -y direction, while one triangle has a leg of 3 in the -x direction and the other a leg of 3 in the +x direction. Notice that the sin(x) is -4/5 for both triangles.

Part A. Quad III: tan(x) = opp/adj = -4/-3 = 4/3
Quad IV: tan(x) = opp/adj = -4/3

Part B. sin(2x) = 2sin(x)cos(x)
Quad III: = 2(-4/5)(-3/5) = 24/25
Quad IV: = 2(-4/5)(3/5) = -24/25

Hope this helps!