Question

find sin(x-y) if sin x=3/5
and tan y = 7/24

Answer 1

What's the formula for sin(x-y)?

Answer 2

sin(x)cos(y)-cos(x)sin(y). I don't know how to put the tan in

Answer 3

How is tan defined?

Answer 4

sin/cos

Answer 5

Can you relate sin to cos another way?

Answer 6

not really

Answer 7

assuming x and y are acute.

Answer 8

answer will be 44/125

Answer 9

how come?

Answer 10

sinx=3/5
tany=7/24
assuming x and y to b acute, u will get cos x=4/5, sin y=7/25, cos y= 24/25
put these values in the formula

Answer 11

u will get the answer

Answer 12

how did you get cos x=4/5?

Answer 13

Did my diagram tell you anything about how sin and cos are related?

Answer 14

hmm... \[\sin^2 +\cos^2=1 \] ?

Answer 15

Yep. So what's cos x if sin x = 3/5?

Answer 16

\[1-(3/5)^2\]

Answer 17

The square root of that. Which is?

Answer 18

AH! 4/5 thank you!

Answer 19

similarly u can get sin y and cos y from the value of tan y

Answer 20

Now, about the y. tan y = 7/24. So how would you get sin y and cos y from that?

Answer 21

hmm...

Answer 22

Remember that sines and cosines are legs of right triangles.

Answer 23

oh! sin y is just 7 and cos is 24 ?

Answer 24

opps oh wait

Answer 25

Yes, except cos and sin are always between -1 and 1. You have to scale them by the hypotenuse.