If A and B are angles between 0 and 90, and sinA = 3/5 and tanB = 7/24, find the value of

sin(A-B).

How do I tackle this question? I just need to know the pathway. Thanks.

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- February 4th 2007, 07:06 AMclassicstringsCompound Angle Forumla
If A and B are angles between 0 and 90, and sinA = 3/5 and tanB = 7/24, find the value of

sin(A-B).

How do I tackle this question? I just need to know the pathway. Thanks. - February 4th 2007, 07:37 AMSoroban
Hello, classicstrings!

Quote:

If and are angles between and ,

and and ,

find the value of

We have the identity: .

We know that: .

We need the values of: .

From and Pythagorus, we find that: .

. . Now you can find

From and Pythagorus, we find that: .

. . Now you can find and

Got it?

- February 4th 2007, 07:47 AMCaptainBlack
First you need to know that:

sin(A-B)=sin(A)cos(B)-cos(A)sin(B).

Then as A and B are both in the range 0 to 90 degrees,

if sin(A)=3/5, then cos(A)=4/5 (there are a number of ways of getting this

result one of which is recognising that A is an angle of a 3,4,5 right triangle

which imediatly tells you that cos(A)=4/5).

if tan(B)=7/24, then sin(B)=7/25, and cos(B)=24/25 (as 25 is the hypotenuse

of a right triangle who's other two sides are 7 and 24).

So:

sin(A-B)=(3/5)(24/25)-(4/5)(7/25)=44/125

RonL