If sin(x) = (3/5) where 90o < x < 180o, then find the exact value of sin(2x). Write in a fraction format: a/b
2007-03-16 16:06:17 · 3 answers · asked by xiuhcoatl 1 in Science & Mathematics ➔ Mathematics
The specified domain makes the angle in quadrant 2. The definition of sine is opp. / hyp. so you can make a right triangle in quad. 2 with length - 4, height 3, and hypotenuse 5 (using Pythagorean Theorem).
Now sin(2x) = 2sin(x)cos(x) ,
from the triangle we made, sin(x) = 3/5, cos(x) = - 4/5
Multiplying gives -24/25.
2007-03-16 16:15:43 · answer #1 · answered by tryzub91 3 · 0⤊ 0⤋
x lies in the 2nd quadrant where sin x = 3/5 and cos x = -4/5.
sin (2x) = 2 sinx cosx = 2(3/5)(-4/5) = -24/25
2007-03-16 23:14:20 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
sin 2x = 2 sinx.cosx
sin2x = 2.(3/5).(-4/5) = - 24/25
2007-03-17 10:37:19 · answer #3 · answered by Como 7 · 0⤊ 0⤋