Question

TOPIC: Trigonometry

GIVEN THE FOLLOWING CONDITIONS:
sin A = 4/5, A Σ I
sin B = -3/5, B Σ III


Find the value of:
I. sin (A +- B)
II. cos (A +- B)
III. tan (A +- B)

Answer 1

@Callisto

Answer 2

@eliassaab

Answer 3

I do not understand what comes after 4/5 and -3/5

Answer 4

let me fix the question

Answer 5

Also look at this summary of trig formulas, your problem follows easily
http://www.math.missouri.edu/escgi/mucgi-bin/trigidentities.cgi

Answer 6

It is still not fixed

Answer 7

it is. see this pic that i will post. it's where i got the question.
wait

Answer 8

You need these formulae

sin(a + b ) = sin(a) cos(b) + sin(b) cos(a)

sin(a - b ) = sin(a) cos(b) - sin(b) cos(a)

cos(a + b ) = cos(a) cos(b) - sin(a) sin(b)

cos(a - b ) = cos(a) cos(b) + sin(a) sin(b)

Answer 9

oh it's (+_)

the plus on top of the minus for I - III

Answer 10

You do first + than -

Answer 11

You need six answers

Answer 12

Where is the picture?

Answer 13

wait. i just took a picture of it

Answer 14

@eliassaab , I think the information beside 4/5 and -3/5 are the position of angle in the cartesian plane. (specifically Quadrant I for <A and Quadrant III for <B

Answer 15

@eliassaab here's the picture

Answer 16

and yes those are values for the carthesian plane @Yttrium

Answer 17

i dont think i have to find 6 answers @eliassaab

Answer 18

somebody. anyone. please help

Answer 19

You really have to find 6 ansers @kaylala.
Let me tell you this:
\[\sin (A \pm B)\] is the notation for\[\sin (A+B)\] and \[\sin(A-B)\]
I hope you understand now.

Answer 20

oh okay i see now @Yttrium

Answer 21

i just dont know how to start this

Answer 22

let's start with angle A

Answer 23

the condition says sinA = 4/5, where it is in quadrant 1.
we know that sinx = opp/hyp
Hence, the figure much look like this.

Answer 24

okay

Answer 25

let's say that adjacent side of A is x.
Can you solve x now?

Answer 26

okay

x=sqrt-9
???
@Yttrium

Answer 27

isn't is sqrt(+9)? which is 3?

Answer 28

oh my bad

Answer 29

it do is 3

Answer 30

Yea it is.
And, with that you can now actually solve for cosA, tanA.

Answer 31

how?

Answer 32

i really dont know how to do this
please guide me
@Yttrium

Answer 33

cosA = adj/hyp
tanA = opp/adj
did you forget that?

Answer 34

sorta

Answer 35

cos A = 3/5
???

Answer 36

tanA=4/3

Answer 37

did i get it?

Answer 38

what do i do next?

Answer 39

You got this. I think it is better if you write sinA, cosA, and tanA in a piece of paper. They are really important later.
Next thing we are going to do is to solve for cosB and tanB

Answer 40

yeah. just wrote it down already

how do i solve for that?

Answer 41

y=4

Answer 42

?
@Yttrium

Answer 43

you sure? isn't it -4? take note it is in the quadrant III.

Answer 44

okay so the quadrant determines the sign?
right?

Answer 45

Yeah. for (x,y)
quadrant I (+,+)
II (-,+)
III (-,-)
IV (+,-)

Now. Find cosB and tanB. Be careful with the signs.

Answer 46

okay then

Answer 47

Solve for cosB and tanB

Answer 48

cos B= -4/5

Answer 49

tanB= 3/-4

Answer 50

Ohhh wait!!!

Answer 51

did i get it?

Answer 52

ookay

Answer 53

the graph will be like this