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.
Hello, classicstrings!
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?
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