Using the Sum to Product Formula
The Sum to Product Formula states the following:
sin(u) + sin(v) = 2sin(a)cos(b)
a and b are defined below:
| a = | u + v |
| 2 |
| a = | 45 + 30 |
| 2 |
| a = | 75 |
| 2 |
a = 37.5
| b = | u - v |
| 2 |
| b = | 45 - 30 |
| 2 |
| b = | 15 |
| 2 |
b = 7.5
Plug in a = 37.5° and b = 7.5°
sin(45) + sin(30) = 2sin(37.5)cos(7.5)
sin(45) + sin(30) = 2(0)(1)
Final Answer
sin(45 + 30) = 0
Common Core State Standards In This Lesson
HSF.TF.C.9
What is the Answer?
sin(45 + 30) = 0
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)
This calculator has 1 input.
* 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)
This calculator has 1 input.
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)
cos(θ) = Adjacent/Hypotenuse
tan(θ) = Opposite/Adjacent
csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)
What 13 concepts are covered in the Sum to Product and Product to Sum Formulas Calculator?
- angle
- the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
- cos
- cos(θ) is the ratio of the adjacent side of angle θ to the hypotenuse
- cos
- cos(θ) is the ratio of the adjacent side of angle θ to the hypotenuse
- cot
- The length of the adjacent side divided by the length of the side opposite the angle. Also equals 1/tan(θ)
- csc
- the length of the hypotenuse divided by the length of the adjacent side. Also equals 1/sin(θ)
- formula
- a fact or a rule written with mathematical symbols. A concise way of expressing information symbolically.
- product
- The answer when two or more values are multiplied together
- sec
- the length of the hypotenuse divided by the length of the adjacent side. Also equals 1/cos(θ)
- sin
- sin(θ) is the ratio of the opposite side of angle θ to the hypotenuse
- sin
- sin(θ) is the ratio of the opposite side of angle θ to the hypotenuse
- sum
- the total amount resulting from the addition of two or more numbers, amounts, or items
- sum to product and product to sum formulas
- tan
- the ratio of the opposite side to the adjacent side of a particular angle of the right triangle.
