Sigma Notation Question/Trig Identity

In summary, The conversation is about deducing the second formula from the first by applying the sum to product identity. The first formula has A=nx and B=x/2 while the second formula has A=(n+1/2)x and B=x/2. The identity used is sin(A)-sin(B)=2cos((A+B)/2)sin((A-B)/2).
  • #1
Lamoid
44
0
[SOLVED] Sigma Notation Question/Trig Identity

I posted this elsewhere but I think I put it in the wrong place so I'm going to post my question again here.


Basically I have to deduce the second formula from the first. Both equations are the same except for the top of the right side, which makes me think it is just a simple matter of a trig identity. Unfortunately, I can't find an identity that would work. Can anyone help?
 

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  • #2
i do not think those formulas are correctly written, i mean the second one. the last part should read like this i guess:

[tex]\frac{sin(\frac{nx}{2})cos(\frac{1}{2}(n+1)x)}{sin\frac{x}{2}}[/tex]

to deduce this one from the first one, you need to apply this rule

[tex]sin(A)-sin(B)=2cos(\frac{A+B}{2})sin(\frac{A-B}{2})[/tex]
 
  • #3
OK, but looking at the first formula, wouldn't A be nx? and B be x/2?

Edit: Ah nvm. OK thank you very much! What is that formula called?
 
Last edited:
  • #4
Lamoid said:
OK, but looking at the first formula, wouldn't A be nx? and B be x/2?

Edit: Ah nvm. OK thank you very much! What is that formula called?

[tex] A=(n+\frac{1}{2})x[/tex]

[tex]B=\frac{x}{2}[/tex]
 
  • #5
It is a "Sum to product identity".
 

Related to Sigma Notation Question/Trig Identity

1. What is sigma notation?

Sigma notation is a mathematical notation used to represent the sum of a series of numbers. It is denoted by the Greek letter sigma (Σ) and has an upper and lower limit to specify the range of values to be summed.

2. How do you simplify a sigma notation expression?

To simplify a sigma notation expression, you can use the properties of sigma notation. These include the commutative property, distributive property, and factoring out a constant. You can also use known summation formulas to simplify the expression.

3. What is the purpose of trigonometric identities?

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables. They are used to simplify and transform trigonometric expressions, making them easier to work with and solve.

4. How do you prove a trigonometric identity?

To prove a trigonometric identity, you need to manipulate one side of the equation using algebraic and trigonometric properties until it is equivalent to the other side. This can involve using reciprocal, quotient, and Pythagorean identities, as well as trigonometric addition and subtraction formulas.

5. What are some common trigonometric identities?

Some common trigonometric identities include the Pythagorean identities (sin²x + cos²x = 1 and tan²x + 1 = sec²x), reciprocal identities (cscx = 1/sinx, secx = 1/cosx, cotx = 1/tanx), and angle sum and difference identities (sin(x ± y) = sinx*cosy ± cosx*siny and cos(x ± y) = cosx*cosy ∓ sinx*siny).

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