Trigonometry

[Stefany]

This is the equation...
This is the formula...
Even with the formula I’m still very confused. I’d love if someone can help!

 

[Dr.Peterson]

What is the question? Were you told to rewrite the given expression as a single trig function, perhaps? Or to find its exact value without using a calculator?

(What you were given is an expression, not an equation; and an expression alone is not a problem. The instructions are an essential part of any problem.)

If so, then you need to apply the angle-sum identity in reverse: The right-hand side looks like the given expression if alpha is 35 and beta is 25; so what does the left-hand side become?

 

[Stefany]

You’re right it’s an expression, you’re suppose to find out what the left side equals using the formula. There weren’t any instructions with it, just the expression with formulas, but I don’t know how to solve it...

 

[Deleted member 4993]

You’re right it’s an expression, you’re suppose to find out what the left side equals using the formula. There weren’t any instructions with it, just the expression with formulas, but I don’t know how to solve it...

If you apply to the second formula:

[math] \alpha = [/math]35^o .............. and .............. [math] \beta = [/math]25^o

What do you get?

 

[MarkFL]

You’re right it’s an expression, you’re suppose to find out what the left side equals using the formula. There weren’t any instructions with it, just the expression with formulas, but I don’t know how to solve it...

What if you let:

[MATH]\alpha=35^{\circ}[/MATH]
[MATH]\beta=25^{\circ}[/MATH]

 

[Stefany]

I’m sorry I don’t understand what you mean... I think the expression is the formula just flipped, so basically I’m suppose to find sin(a+b). But both angels are different so I don’t know how it’s going to work.

 

[Deleted member 4993]

I’m sorry I don’t understand what you mean... I think the expression is the formula just flipped, so basically I’m suppose to find sin(a+b). But both angels are different so I don’t know how it’s going to work.

What is

35+25 = ?

 

[MarkFL]

I’m sorry I don’t understand what you mean... I think the expression is the formula just flipped, so basically I’m suppose to find sin(a+b). But both angels are different so I don’t know how it’s going to work.

According to the angle sum identity for sine that you posted, we may write:

[MATH]\sin(35^{\circ}+25^{\circ})=\sin(35^{\circ})\cos(25^{\circ})+\cos(35^{\circ})\sin(25^{\circ})[/MATH]
Or:

[MATH]\sin(60^{\circ})=\sin(35^{\circ})\cos(25^{\circ})+\cos(35^{\circ})\sin(25^{\circ})[/MATH]
Can you proceed?

 

[Stefany]

Ok, but do you then divide it?

 

[MarkFL]

Divide what?

 

[Stefany]

Never mind, I got confused.

 

[Deleted member 4993]

Never mind, I got confused.

So you have solved the problem. Good!

What "exact" Numerical answer did you get for:

sin(35^∘) * cos(25^∘) + cos(35^∘) * sin(25^∘) = ?

There is an "exact" answer.