# Math Help - Compound Angle

1. ## Compound Angle

Angle a lies in the second quadrant and angle b lies in the third quadrant such ath cos a = -3/5 and tan b = 24/7

determine an exact value for
cos(a+b)
and
sin (a-b)

I got cos(a+b) = cosacosb - sinasinb
=(-3/5)(-7/25) - (4/5)(-24/25)
= 117/125

i am not sure if this is right, but i am also completely lost for sin (a-b)

2. Originally Posted by Johnny123321
Angle a lies in the second quadrant and angle b lies in the third quadrant such ath cos a = -3/5 and tan b = 24/7

determine an exact value for
cos(a+b)
and
sin (a-b)

I got cos(a+b) = cosacosb - sinasinb
=(-3/5)(-7/25) - (4/5)(-24/25)
= 117/125

i am not sure if this is right, but i am also completely lost for sin (a-b)
It will help if you recall the 3-4-5 Right-angle triangle, and the 7-24-25 Right-angle triangle.

3. ## check

can you help me check if i did cos (a+b) right

4. Originally Posted by Johnny123321
Angle a lies in the second quadrant and angle b lies in the third quadrant such ath cos a = -3/5 and tan b = 24/7

determine an exact value for
cos(a+b)
and
sin (a-b)

I got cos(a+b) = cosacosb - sinasinb
=(-3/5)(-7/25) - (4/5)(-24/25)
= 117/125

i am not sure if this is right, but i am also completely lost for sin (a-b)
If $a$ is in quadrant 2, then $\sin{a} > 0, \cos{a} < 0$ and $\tan{a} < 0$.

If $b$ is in quadrant 3, then $\sin{b} < 0, \cos{b} < 0$ and $\tan{b} > 0$.

If you remember this as well as the 3-4-5 Right-angle triangle and the 7-24-25 Right-angle triangle, you will be fine.

5. The first part looks correct to me.

$sin(A-B)=sinAcosB-sinBcosA$
$(4/5)(-7/25)-(-24/25)(-3/5)$
$(-21/25)-(72/125)$
$(-93/125)$