# Thread: [SOLVED] Given sin A and sin B, find without using a calculator.

1. ## [SOLVED] Given sin A and sin B, find without using a calculator.

Given that A and B are acute angles with cos A = 4/5 and sin B = 5/13, find without using tables or a calculator

cos (A + B)

Here is my take on the question.

cos (A + B)
= cosAcosB - sinAsinB
= (4/5)cosB - sinA(5/13)

After this, I don't know how to continue. Answer is 33/65

2. Presumably you do know that $cos^2(A)+ sin^2(A)= 1$ and $cos^2(B)+ sin^2(B)= 1$. Since you know sin(B) and cos(A) (and know that the angles are acute) you can solve for cos(B) and sin(A).

3. Originally Posted by mark1950
Given that A and B are acute angles with cos A = 4/5 and sin B = 5/13, find without using tables or a calculator

cos (A + B)

Here is my take on the question.

cos (A + B)
= cosAcosB - sinAsinB
= (4/5)cosB - sinA(5/13)

After this, I don't know how to continue. Answer is 33/65
$\cos^2 A + \sin^2 A = 1$. You know the value of $\cos A$ and you know that $A$ is in the first quadrant. So get the value of $\sin A$ ....

$\cos^2 B + \sin^2 B = 1$. You know the value of $\sin B$ and you know that $B$ is in the first quadrant. So get the value of $\cos B$ ....

4. Originally Posted by mark1950
Given that A and B are acute angles with cos A = 4/5 and sin B = 5/13, find without using tables or a calculator

cos (A + B)

Here is my take on the question.

cos (A + B)
= cosAcosB - sinAsinB
= (4/5)cosB - sinA(5/13)

After this, I don't know how to continue. Answer is 33/65
HI

good start . You are told that both angles are acute ie <90 which means they are both in the first quadrant .

Draw a triangle .. with sides 3 , 4 , 5

sin A = 3/5

Same goes to the other one . cos B=12/13

Then put them together .

5. Thanks, guys! Finally found the answer.