maths trig help (1 Viewer)

[annihilator1]

could someone please show me working out to these 2 question?
if sin A=4/5 and sin B=5/13, find:
(i) sin (A+B)
(ii) cos(A-B)
when 0<A<90 degrees and 0<B<90

the answers says:
(i) is 63/65
(ii) is 56/65

Thanks in advance

 

[SpiralFlex]

could someone please show me working out to these 2 question?
if sin A=4/5 and sin B=5/13, find:
(i) sin (A+B)
(ii) cos(A-B)
when 0<A<90 degrees and 0<B<90

the answers says:
(i) is 63/65
(ii) is 56/65

Thanks in advance

I drew a pretty diagram for you. By using Pythagoras we can find the missing values. Since the restriction is given, it is advisable to draw a general triangle in the first quadrant.







i. Let's expand.








ii.

 

[Parvee]

for (i) you use sin(a+b)=sinAcosB+cosAsingB
-to work out cos a and b draw the triangles and work it out with pythag
ends up to be 4/5 x 12/13 + 3/5 x 5/13 = 63/65

for (ii) you use cos(A-B) = cosAcosB+sinAsinB
ends up to be 3/5 x 12/13 + 4/5 x 5/13 = 56/65

 

[Parvee]

damn spiral beat me to it :L

 

[SpiralFlex]

damn spiral beat me to it :L

Let me eat you human!

 

[annihilator1]

thanku
appreciated
btw would any of you have a file of fully worked solutions for couchman and jones 3 unit book 2?

 

[Parvee]

nope :/
not sure about spiral though, his loaded with resources :L

 

[annihilator1]

how about this question...
if A and B are acute angles with sin A=3/5 and sin B=1/2,evaluate:
(i) sin(A+B)
(ii) cos(A-B)

answer to:
(i) is (3root3 + 4)/10 and
(ii) is (4root3 + 3)/10

 

[annihilator1]

please helpp

 

[Aysce]

Just do the same things as the questions above, but if you want I shall do it

 

[SpiralFlex]

how about this question...
if A and B are acute angles with sin A=3/5 and sin B=1/2,evaluate:
(i) sin(A+B)
(ii) cos(A-B)

answer to:
(i) is (3root3 + 4)/10 and
(ii) is (4root3 + 3)/10

I drew you another pretty diagram.







Remember acute angles are in the first quadrant!

i.

From our first diagram,






ii.

From our second digram,





I only have the Year 12 Couchman solutions, some of it. I think it's a violation if I upload them.