Question

If sin A = 4/5 and A is in Quadrant 2, and sin B =5/12 and B is in Quadrant 1, find the exact value of

Sin (A-B)

Answer 1

are you sure that sin B isn't 5/13? (5-12-13 triangle)

Answer 2

im sure its not

Answer 3

i think it must be otherwise we cant get an exact value

Answer 4

ok my homework says 5/12 maybe thats a typo so lets assume its 5/13...what do we do

Answer 5

ok

then cos b = 12/13 , and cos a = -3/5 as its in 2nd quadrant

so plud these values into the the identity

sin (a-b) = sina cos b - cos a sin b
= 4/5 * 12/13 -[ (-3/5 * 5/12)
= 48/65 + 15/60

Answer 6

= 48/65 + 1/4
= 192/260 + 65/260
= 257 / 260

Answer 7

ok is that it?

Answer 8

yes

Answer 9

thanks very much

Answer 10

i have one similar if you dont mind

Answer 11

what if it was cos(A + B)

Answer 12

ok
cos (a + b) = cosa cosb - sina sinb

= 12/13 * -3/5 - 5/13 * 4/5
= -36/65 - 20/65 = -56/65

Answer 13

oh - theres an error in sin(a-b) - i used 5/12 instead of 5/13
so correct is

sin (a-b) = 4/5 * 12/13 -[ (-3/5 * 5/13)

= 48/65 + 15/65 = 63/65

Answer 14

thanks very much..i have one last one...what if its tan(b/2)

Answer 15

tan(b/2) - i cant remember the identity - ley me check it out - give me a few minutes

Answer 16

ok

Answer 17

sorry jinnie i cant dig it out and i have to leave - theres is an identity linking tan (b/2) to sin b and cos b. you just need to plug in the values yu've got already

Answer 18

ok thanks for the help

Answer 19

yw

Answer 20

i didnt have to be away for long
and
i remembered the formula

tan(b/2) = sin b / (1 + cos b) = 5/13 / ( 1 + 12/13)
= 5/13 / 25/13 = 5/13 * 13/25 = 1/5

Answer 21

ok thanks very much

Answer 22

these are all the questions i have pertaining to this concept...i still have other question but they are completely different concepts...would you be willing or do you have the time to help me more?