SOLUTION: find the exact value of sin(x-y) if sin x = 4/9 and sin y = 1/4

Question 1154735: find the exact value of sin(x-y) if sin x = 4/9 and sin y = 1/4

Found 3 solutions by greenestamps, MathLover1, ikleyn:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

There is not enough information to find the exact value.

Given sinx = 4/9, we know cosx is EITHER sqrt(65)/9 OR -*sqrt(65)/9;
given siny = 1/4, we know cosx is EITHER sqrt(15)/4 OR -sqrt(15)/4.

Since there is no information allowing us to determine which values to use for cosx and cosy, we can't find the value of sin(x-y).

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

the exact value of
if and
use identities:

and

if , then
=>

Therefore,

-> the exact value

Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.

In order for this problem (and many other similar problems) be correctly posed, it MUST say to which quarter
every of the angles x and y do belong.

RELATED QUESTIONS
Find the exact value of sin (x+y) if sin x = 4/5 in Quadrant II and tan y = 12/5 in... (answered by lwsshak3)
Find the exact value if 0 < x < pi/2 and 0 < y < pi/2 ; sin(x+y) if sin(x) = 3/5 and... (answered by fractalier)
If sin x<0 and tan x=-4/5, find the exact value of sec x (answered by lwsshak3)
if sec(x) = -5/4 and sin(x) < 0, find the exact value of... (answered by harpazo,lwsshak3)
If x is in the first and y is in the second quadrant, sin = 24/25, and sin y = 4/5, find... (answered by Edwin McCravy)
find sin(x+y) if sin x=2/3 and sin y=... (answered by jsmallt9)
y- -4 sin... (answered by Fombitz)
y= 4... (answered by Alan3354)
Assume 3 cos(x) − 4 sin(x) = 4 and 4 cos(x) + 3 sin(x )= 3 Find the exact... (answered by AnlytcPhil)