SOLUTION: Hi, i'm just not sure how to even start this problem? Thanks for the help! Given alpha, beta [0,pi/2], sin alpha= 1/3, sin beta= 1/4, find the exact value of sin(alpha + beta)

Question 437992: Hi, i'm just not sure how to even start this problem? Thanks for the help!
Given alpha, beta [0,pi/2], sin alpha= 1/3, sin beta= 1/4, find the exact value of sin(alpha + beta)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Given alpha, beta [0,pi/2], sin alpha= 1/3, sin beta= 1/4,
find the exact value of sin(alpha + beta)
----
sin(a) = 1/3 means y = 1 when r = 3.
Solve for "x": x^2 = 3^2-1^2 = 8
So x = 2sqrt(2)
---
Therefore cos(a) = x/r = (2sqrt(2))/3
------------------------------------------
sin(b) = 1/4 means y = 1 when r = 4
Solve for "x": x^2 = 4^2-1^2 = 15
So x = sqrt(15)
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Therefore cos(b) = x/r = sqrt(15)/4
------------------------------------------
Formula: sin(a + b) = sin(a)cos(b)+cos(a)sin(b)
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= (1/3)(sqrt(15)/4) + (2sqrt(2)/3)(1/4)
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= sqrt(15)/12 + 2sqrt(3)/12
------
= [sqrt(15)+2sqrt(3)]/12
============================
Cheers,
Stan H.

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