Question

If sin(x) = 1/3 and sec(y) = 25/24, where x and y lie between 0 and π/2, evaluate the expression using trigonometric identities.
sin(x + y)

Answer 1

do you know formula sin(a+b) = ?

Answer 2

@OtherWorldly

Answer 3

Yes sin A cos B + cos A sin B ? @jhonyy9

Answer 4

and sec(y) = ?

Answer 5

1/cos

Answer 6

@jackthegreatest

Answer 7

ok

evaluate using this values the sin(x+y) formula

Answer 8

1/cos = 25/24 -- given

than cos = ?

Answer 9

ummm. 24/25?
so would the formula then be:
sin(1/3)cos(24/25) + sin(24/25)cos(1/3) ?

Answer 10

you not are sure in this ? why ?

Answer 11

um... what? LOL

Answer 12

this would be in radians, correct?

Answer 13

@jhonyy9 the sum and difference formula?

Answer 14

@jackthegreatest so then, using that formula, would my answer be correct? sin(1/3)cos(24/25) + sin(24/25)cos(1/3)?
(in radians)

Answer 15

how you understand this << sum and difference >> ?

Answer 16

@jhonyy9 well thats what precalc textbooks call it

Answer 17

@zepdrix please do you understand this ?

Answer 18

sin(x+y)

so we need using here the sum just and not the difference - why said it so ?

Answer 19

i'm so lost omg

Answer 20

@jhonyy9 btw, those are angles

Answer 21

@jackthegreatest you wrote it hence above - please clarify

Answer 22

degrees

Answer 23

@zepdrix sorry ,do you understand this ,,difference" what mean here ?

Answer 24

@jhonyy9 what would be best for kwonbon is if you just worked out the problem

Answer 25

we need just giving the way ,help the askers understanding how he or she can solving the posted exercise and not solve from start till the end this exercise,problem or question

hope you know it sure

Answer 26

@zepdrix do you agree this please ?

Answer 27

@jhonyy9 but you're not even helping me LOL it feels like you don't even know how to do the problem yourself...

Answer 28

like you don't even answer the questions i ask in response to your questions that you ask me

Answer 29

than you check there above i drived you step by step - yes ? and o ve got the formula sin(x+y) = ?

Answer 30

._. yes

Answer 31

so then i asked you if it was sin(1/3)cos(24/25) + sin(24/25)cos(1/3)

Answer 32

no

bc. given that sin x = 1/3 or cos x = 24/25

Answer 33

Oh sorry I ran off :3

Answer 34

there you need substituting the sinx by 1/3 not sin1/3
and same the cos x

Answer 35

So we agreed that the Angle Addition Formula would be useful here,\[\large\rm \sin(x+y)=\color{orangered}{\sin x} \cos y+\sin y \cos x\]Look at this thing in orange a sec.

They gave us this information at the very start.\[\large\rm \color{orangered}{\sin x=\frac13}\]This is telling us that we can replace sinx with 1/3 in our expansion,\[\large\rm \sin(x+y)=\color{orangered}{\frac13} \cos y+\sin y \cos x\]Kwon, does that help you to understand why your answer was nonsense?
There shouldn't be a sin in front of your 1/3 anymore.

Answer 36

Oh he left :( ugh

Answer 37

thank you zepdrix

Answer 38

@jackthegreatest do you understand it now ?

Answer 39

what you mean if i understand it now?

Answer 40

how you get the right answer ?

Answer 41

when evaluate the sin(x+y) so there you need writing not sinx just 1/3 bc. sin x =1/3 and cos x = 24/25

Answer 42

@kwonbon

Answer 43

haha you realize all i was saying is that x and y are degrees

Answer 44

what i dont understand that why wrote there above the sum and difference when here need using just the sum ?

Answer 45

\[\sin \left( x+y \right)=\sin x \cos y+\cos x \sin y\]
\[\sin x=\frac{ 1 }{ 3 },\cos x=\sqrt{1-\sin ^2x}=\sqrt{1-\frac{ 1 }{ 9 }}=\sqrt{\frac{ 8 }{ 9 }}=\frac{ 2\sqrt{2} }{ 3 }\]
\[\cos y=\frac{ 24 }{ 25 },\sin y=\sqrt{1-\frac{ 576 }{ 625 }}=\sqrt{\frac{ 49 }{ 625 }}=\frac{ 7 }{ 25 }\]

Answer 46

plug the values in the formula
and find sin(x+y)

Answer 47

Have a look at "sin(1/3)cos(24/25) + sin(24/25)cos(1/3)." You are told that sin x =1/3 and sec y=24/25. The sum formula for the sine function requires sin x, cos y, sin y and cos x. Where are you going to get these values for these four?

The value of sin x is given: sin x = 1/3. Here, x is an angle and 1/3 is the value of the sine function. So writing sin(1/3) makes no sense. What you want to do is to replace sin x in the sum formula with 1/3.

The value of sec y is given: 25/24. Taking the reciprocal of both sides, cos y=24/25.

Do not write cos (24/25); instead, substitute 24/25 for cos y.

Can you find sin y? Can you find cos x?

Can you now complete the problem?

Answer 48

Acknowledging that sshayer has already found the values of all four necessary trig functions.