Question

Given:
sin(x) = 2/3 and cos(y) = 3/4

Find the values of:
a) sin(x+y)
b) cos(x-y)
c) tan(x+y)

Answer 1

I can't seem to find x and y

Answer 2

^Exact values btw

Answer 3

Consider 2 different right angled triangles with two of the sides as mentioned in the question.

Answer 4

How does this give x and y? I need exact values

Answer 5

Hang on, I'm working on it.

Answer 6

inverse functions for cosine and sine

Answer 7

Yeah, but as I mentioned, I need exact values

Answer 8

sin(x+y)=sinx*cosy+cox*siny

Answer 9

how do i get cos x and sin y?

Answer 10

sinx=2/3
so cosx= sqrt(1-(sinx)^2)

Answer 11

similarly, siny= sqrt(1- (cosy)^2)

Answer 12

sin(x+y) is quite easy. Use the identity that @vedic mentioned. You already know sin(x) and cos(y) from the question.
Then you need right angled triangles or follow @vedic's instructions.
The first two answers should be 1, the last one should be 8.4. (Please confirm the last one, as I'm unsure.)

Answer 13

Thanks guys

Answer 14

I'll work on it

Answer 15

for tan(x+y).. u cn simply divide sin(x+y) and cos(x+y)

Answer 16

formulas u cn find frm dis list...

Answer 17

@tommo_lcfc how u getting answer 1?

Answer 18

\[\frac{6+\sqrt{35}}{12}\]

Answer 19

yeaahh thts the answer...

Answer 20

working on no. 2 now

Answer 21

\[\frac{3\sqrt{5}+2\sqrt{7}}{12}\]

Answer 22

no.3 \[\frac{6+\sqrt{35}}{3\sqrt{5}-2\sqrt{7}}\]

Answer 23

ryt... someone here wants to understand and do things... i appreciate that..:)

Answer 24

Thanks heaps :D