sin(45)sin(30) ·

12 Sep 2024, 00:00

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Using Product to Sum Formula

The Product to Sum Formula states the following:

Use a trig identity:

Sin(u)Sin(v) =	Cos(u - v) - Cos(u + v)
	2

In this case, u = 45 and v = 30

Sin(45)Sin(30) =	Cos(45 - 30) - Cos(45 + 30)
	2

Sin(45)Sin(30) =	Cos(15) - Cos(75)
	2

Sin(45)Sin(30) =	0.96592582636649 - 0.2588190465473
	2

Sin(45)Sin(30) =	0.70710677981919
	2

Final Answer

Sin(45)Sin(30) = 0.3535533899096

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What is the Answer?

Sin(45)Sin(30) = 0.3535533899096

How does the Sum to Product and Product to Sum Formulas Calculator work?

Free Sum to Product and Product to Sum Formulas Calculator - Given two angles in degrees of u and v, this determines the following:
* Sin(u) ± Sin(v)
* Cos(u) ± Cos(v)
* Sin(u)Sin(v)
* Cos(u)Cos(v)
* Sin(u)Cos(v)
* Cos(u)Sin(v)
* Sin(u + v)
* Sin(u - v)
* Cos(u + v)
* Cos(u - v)
* Tan(u + v)
* Tan(u - v)
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What 9 formulas are used for the Sum to Product and Product to Sum Formulas Calculator?

sin(θ) = Opposite/Hypotenuse
cos(θ) = Adjacent/Hypotenuse
tan(θ) = Opposite/Adjacent
csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)

For more math formulas, check out our Formula Dossier

What 13 concepts are covered in the Sum to Product and Product to Sum Formulas Calculator?

anglethe figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. coscos(θ) is the ratio of the adjacent side of angle θ to the hypotenusecoscos(θ) is the ratio of the adjacent side of angle θ to the hypotenusecotThe length of the adjacent side divided by the length of the side opposite the angle. Also equals 1/tan(θ)cscthe length of the hypotenuse divided by the length of the adjacent side. Also equals 1/sin(θ)formulaa fact or a rule written with mathematical symbols. A concise way of expressing information symbolically.productThe answer when two or more values are multiplied togethersecthe length of the hypotenuse divided by the length of the adjacent side. Also equals 1/cos(θ)sinsin(θ) is the ratio of the opposite side of angle θ to the hypotenusesinsin(θ) is the ratio of the opposite side of angle θ to the hypotenusesumthe total amount resulting from the addition of two or more numbers, amounts, or itemssum to product and product to sum formulastanthe ratio of the opposite side to the adjacent side of a particular angle of the right triangle.

sin(45)sin(30)

The Product to Sum Formula states the following: Sin(45)Sin(30) = 0.3535533899096 What is the Answer? Sin(45)Sin(30) = 0.3535533899096 How does the Sum to Product and Product to Sum Formulas Calculator work?