SOLUTION: find the exact value of the trigonometric expression given that tanA=3/4 and cosB=-4/5, A is in Quadrant 1 and pi < B

Click here to see ALL problems on Trigonometry-basics

Question 1117332: find the exact value of the trigonometric expression given that tanA=3/4 and cosB=-4/5, A is in Quadrant 1 and pi < B < 3pi/2
The problem is sin(A+B)
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
find the exact value of the trigonometric expression given that tanA=3/4 and cosB=-4/5, A is in Quadrant 1 and pi The problem is sin(A+B)
----
Sin(A+B) = sin(A)cos(B)+sin(B)cos(A)
-----
Since tan(A)=(y/x) = 3/4), sin(A) = (y/r) = 3/sqrt(3^2+4^2) = 3/5
and cos(A) =(x/4) = 4/5
---
Since cos(B)= (x/r) = -4/5, sin(B)=(y/r) = sqrt(5^2-4^2)/5 = 3/5
----
Ans: sin(A+B) = (3/5)(-4/5) + (3/5)(4/5) = 0
-----
Cheers,
Stan H.
------------

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Use a similar argument to demonstrate:

And once more:

======================

Plug in the numbers and do the arithmetic. Mind your signs

John

My calculator said it, I believe it, that settles it

SOLUTION: find the exact value of the trigonometric expression given that tanA=3/4 and cosB=-4/5, A is in Quadrant 1 and pi < B < 3pi/2 The problem is sin(A+B)