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Use the sum-to-product formula to write the sum as a product: sin(3)+sin(). Evaluate cos(15°)cos(75°). Check the answer with a graphing calculator. We begin by writing the formula for the difference of cosines.
In math, when we use the word “sum,” we mean add the numbers. When we use the word “product,” we mean multiply the numbers. So the “sum of the products” means we want to add (sum) the results of numbers being multiplied (products). Let me give you an example.
Sum of Cosine and Sine We show this by using the principle cos =sin (/2), and convert the problem into the sum (or difference) between two sines. We note that sin /4=cos /4=1/2, and re-use cos =sin (/2) to obtain the required formula.
In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.
6:42 11:59 Suggested clip Sum to Product Identities and Product to Sum Formulas — Trig YouTubeStart of suggested client of suggested clip Sum to Product Identities and Product to Sum Formulas — Trig
Expressing the Product of Sine and Cosine as a Sum Then substitute the given values into the formula and simplify. Use the product-to-sum formula to write the product as a sum: sin(x+y)cos(XY).
The PRODUCT function works with arrays, but it doesn't require the normal array syntax (Ctrl + Shift + Enter) to enter. The purpose of the PRODUCT function is to multiply, then sum, arrays. If only one array is supplied, PRODUCT will simply sum the items in the array. Up to 30 arrays can be supplied.
The word product means the results of multiplying two or more numbers. The word sum means the results of adding two or more numbers.
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