# Addition formulae - Trig help requested

• kalistella
In summary, the conversation is about a request for help with trigonometry, specifically regarding the addition formula for sine and cosine. The person is struggling with solving problems involving angles of 120 degrees and is seeking guidance from others. They have made a mistake in their application of the addition formula and are advised to review it and consider using fundamental angles to solve the problem.
kalistella
addition formulae - Trig help requested!

I have a problem with this with regard to Sin 120 or Cos 120.

Eg

sin 165
sin (120 +45)
sin120.cos45-cos120.sin45

How do I deal with sin 120 or cos 120?

I know that cos 45 is 1/square root 2 and so is sin 45.

But in the above problem, the answer comes to 1/4 (square root 6 - square root 2)

I don't get this answer. My problem is with the 120 angles.

Thanks!

Well, learn the correct addition formula properly.
Then, look at the unit circle what sin(120) and cos(120) should be.

kalistella said:
sin (120 +45)
sin120.cos45-cos120.sin45

marlon

As arildno and marlon have already pointed out, you have the sine sum formula wrong! As for 120 degrees what fundamental angles do you know sine and cosine for? (You seem to have 45 degrees okay.) Would it help to remember that 120= 60+ 60 or that 120= 90+ 30?

## 1. What is the addition formula for sine?

The addition formula for sine is sin(A + B) = sinA cosB + cosA sinB.

## 2. How do I use the addition formula for cosine?

To use the addition formula for cosine, you need to know the values of the angles A and B. Then, you can plug those values into the formula cos(A + B) = cosA cosB - sinA sinB and solve for the resulting value.

## 3. Can the addition formula be used for tangent?

Yes, the addition formula can also be used for tangent. The formula is tan(A + B) = (tanA + tanB) / (1 - tanA tanB).

## 4. How do I remember all the addition formulae for trigonometric functions?

One helpful way to remember the addition formulae for trigonometric functions is to use the acronym "SOHCAHTOA" which stands for "sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent." This can help you remember the relationships between the functions and how they can be used in the addition formulae.

## 5. Are there any other useful trigonometric formulae related to addition?

Yes, there are other useful trigonometric formulae related to addition, such as the double angle formulae and the half angle formulae. These formulae can be used to simplify and solve trigonometric equations involving addition of angles.

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