Quote:
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!