Question

if x is in the first and y in the third quadrant, sinx=3/5, and cosy=-5/13, find the exact value of sin(x+y), cos(x+y), and tan(x+y)?

Answer 1

well you need a simple quadrant drawing with some additional information



once you have a and b, then you can use the expansions for sin, cos and tan

then substitute the necessary exact values... and simplfy

Answer 2

how to find a & b?

Answer 3

do you know pythagoras' theorem..?

Answer 4

yes I do

Answer 5

ok... you can find a and b using pythagoras, and as it says in the drawing, they are both negative, because of where they are on the number plane.

then when you have them

for x you can now find cos and tan

and for y

you can find sin and tan

then you can get the expansions...

Answer 6

can u help me more :(

Answer 7

\[a^2+3^2=5^2 \therefore a=4,
\[\therefore b=12\]

Answer 8

I did that and next what ?

Answer 9

cos(x+y) = cos(x)cos(y) - sin(x)sin(y)

Answer 10

?

Answer 11

and then ?

Answer 12

just find cos(x),sin(x),sin(y),cos(y) ...... using the formula as sin = opp/hyp, cos=adj/hyp..... finally tan(x+Y)= sin(x+y)/cos(x+y) ..... u wl get the answer ...

Answer 13

what is the x and what is y ??

Answer 14

sin(X)=3/5, cos(x)=-4/5, sin(y)=12/13, cos(y)= -5/13

Answer 15

the diagram seems to be wrong i think ....