Trigonometry question

[PolySquared]

Hi guys,

Can someone please help me solve this question?

If sin(U) = 12/13 and sin(V) = 3/5, evaluate sin(U+V)

[VanillaRice]

What progress have you made so far?
Hint: You'll need to use the compound angle formula for sine. But then, we need cos(U) and cos(V) as well! How can find a value for the cosine of an angle, given its sine value?

Post if you get stuck

[PolySquared]

What progress have you made so far?
Hint: You'll need to use the compound angle formula for sine. But then, we need cos(U) and cos(V) as well! How can find a value for the cosine of an angle, given its sine value?

Post if you get stuck

I got the answer as 63/65, but the textbook says there are 4 answers.

[jazzycab]

I got the answer as 63/65, but the textbook says there are 4 answers.

There are multiple answers as there is no specification on the domain for either angle U or V. That is, although we know that sine of both angles is positive, cos of either angle could be positive or negative. Therefore, you should get an answer for:
- cos(U)>0 AND cos(V)>0
- cos(U)>0 AND cos(V)<0
- cos(U)<0 AND cos(V)>0
- cos(U)<0 AND cos(V)<0

[PolySquared]

There are multiple answers as there is no specification on the domain for either angle U or V. That is, although we know that sine of both angles is positive, cos of either angle could be positive or negative. Therefore, you should get an answer for:
- cos(U)>0 AND cos(V)>0
- cos(U)>0 AND cos(V)<0
- cos(U)<0 AND cos(V)>0
- cos(U)AND cos(V)<0

thanks for the response. Do you know how to solve this?

Simplify this
Cos(U-V)Sin(V)+Sin(U-V)Cos(V)

I have no idea how to approach this. 

[jazzycab]

thanks for the response. Do you know how to solve this?

Simplify this
Cos(U-V)Sin(V)+Sin(U-V)Cos(V)

I have no idea how to approach this. 

The problem with questions of this type is that we don't necessarily know what could be considered 'simpler', but for the purpose of doing something with this:
Try and expand the two terms with arguments U-V using compound angle formulas. After that, you may find that some like terms cancel, otherwise, you may then need to use the trigonometric identity to progress further.

[PolySquared]

The problem with questions of this type is that we don't necessarily know what could be considered 'simpler', but for the purpose of doing something with this:
Try and expand the two terms with arguments U-V using compound angle formulas. After that, you may find that some like terms cancel, otherwise, you may then need to use the trigonometric identity to progress further.

Thanks bro. I understand now.