To do these type of problems, you need to know the following:
the expansion of
1. sin(A+B) = sinAcosB + cosAsinB
2. cos(A+B) = cosAcosB - sinAsinB
3. and tan(A+B) = (tanA + tanB)/( 1 - tanAtanB)
4. the CAST rule
5. the definitions of the basic trig ratios based on the sides
of a right-angled triangle
given: cos A = -3/5 , cosA = adjacent/hypotenuse and A is in III
so sinA = -4/5 , tanA = 4/3
tan B = 7/24, B is in I, so sinB = 7/25 and cosB = 24/25
sin(A+B) = (-4/5)(24/25) + (-3/5)((7/25) = -117/125
do the others in the same way.
You can always check your answers with your calculator,
my sin(A+B) is correct after checking.
Given cos A = -3/5, π<A<3π/2, and tan B = 7/24, B in Quadrant I, find: (a) sin (A+B), (b) cos (A+B), and (c) tan (A+B)
2 answers
Thank you