SOLUTION: Let sin s = (-1/4), with s in quadrant 4 and cos t = (-4/5), with t in quadrant 2. Find sin(s+t) and explain.

Algebra ->  Trigonometry-basics -> SOLUTION: Let sin s = (-1/4), with s in quadrant 4 and cos t = (-4/5), with t in quadrant 2. Find sin(s+t) and explain.      Log On


   

Question 823644: Let sin s = (-1/4), with s in quadrant 4 and cos t = (-4/5), with t in quadrant 2.
Find sin(s+t) and explain.
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Let sin(s) = (-1/4), with s in quadrant 4
and cos(t) = (-4/5), with t in quadrant 2.
-----
Find cos(s)::
Since sin(s) = y/r = -1/4, y = -1 and r = 4
Therefore x = sqrt[4^2-1^2] = sqrt(15)
And cos(s) = x/r = sqrt(15)/4
-------------------------------------------
Find sin(t)::
Since cos(t) = x/r = -4/5, x = -4 and r = 5
Therefore y = sqrt[5^2-4^2] = 3
So sin(t) = y/r = 3/5
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Find sin(s+t) = sin(s)cos(t)+cos(s)sin(t)
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= (-1/4)(-4/5)+(sqrt(15)/4)(3/5)
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= (1/5)+(3sqrt(15)/20)
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= [4+3sqrt(15)]/20
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= 0.7809
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The angle whose sin is +.25+ is +14.478+ degrees
+360+-+14.478+=+345.522+ which places it in the 4th quadrant
+s+=+345.522+
--------------------
The angle whose cosine is +4%2F5+ is +36.870+ degrees
+180+-+36.870+=+143.130+ which places it in the 2nd quadrant
+t+=+143.130+
--------------------
+sin%28+s+%2B+t+%29+=+sin%28+345.522+%2B+143.130+%29+
+sin%28+s+%2B+t+%29+=+sin%28+488.652+%29+
+sin%28+s+%2B+t+%29+=+sin%28+3%2A180+-+488.652+%29+
( this shows that the angle ends up in the 2nd quadrant )
+sin%28+s+%2B+t+%29+=+sin%28+540+-+488.652+%29+
+sin%28+s+%2B+t+%29+=+sin%28+51.348+%29+
+sin%28+51.348+%29+=+.781+
( note that the sin is positive in the 2nd quadrant