Using the Sum to Product FormulaCalculate Cos(45°) + Cos(30°)
Table of Contents
The Sum to Product Formula Formula states the following:
Cos(u) + Cos(v) = 2cos(a)cos(b)a and b are defined below:| a = | u + v |
| 2 |
| a = | 45 + 30 |
| 2 |
| a = | 75 |
| 2 |
| b = | u - v |
| 2 |
| b = | 45 - 30 |
| 2 |
| b = | 15 |
| 2 |
With a = 37.5° and b = 7.5°, we havecos(45) + sin(30) = 2cos(37.5)cos(7.5)cos(45) + sin(30) = 2(1)(1)
cos(45 + 30) = 2
What is the Answer?
cos(45 + 30) = 2
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.
What 9 formulas are used for the Sum to Product and Product to Sum Formulas Calculator?
sin(θ) = Opposite/Hypotenusecos(θ) = Adjacent/Hypotenusetan(θ) = Opposite/Adjacentcsc(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?
- 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.
