Problem involving Power-Reducing Formula

  • Thread starter DinosaurEgg
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In summary, the Power-Reducing Formula, also known as the double-angle formula, is a mathematical identity that simplifies trigonometric expressions involving powers of sine and cosine. It can be derived using trigonometric identities and the laws of exponents, making it a useful tool for solving complex equations and simplifying expressions. This formula can be applied in a variety of trigonometric problems, such as finding exact values of functions, simplifying expressions, and proving identities. However, it has limitations and can only be used for functions involving sine and cosine. It can also be applied in scientific fields such as physics, engineering, and astronomy to solve problems related to periodic motion, oscillations, and waves.
  • #1
DinosaurEgg
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Homework Statement


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Homework Equations


How in the world did they get their solution? Where did 27/8 come from?


The Attempt at a Solution


I did the arithmetic with the fractions inside before distributing the 9, and ended up getting something like -9/4 cos2x + 9/4 cos4x. Completely different from theirs.
 
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  • #2
In the step above that, you have 1/4 + 1/8 = 2/8 + 1/8 = 3/8, then times 9 is 27/8
 

1. What is the Power-Reducing Formula?

The Power-Reducing Formula, also known as the double-angle formula, is a mathematical identity that allows us to simplify trigonometric expressions involving powers of sine and cosine.

2. How is the Power-Reducing Formula derived?

The Power-Reducing Formula can be derived using various trigonometric identities and the laws of exponents. It is a useful tool for solving complex trigonometric equations and simplifying expressions.

3. What types of problems can be solved using the Power-Reducing Formula?

The Power-Reducing Formula can be used to solve a variety of trigonometric problems, such as finding exact values of trigonometric functions, simplifying expressions, and proving identities.

4. Are there any limitations to using the Power-Reducing Formula?

While the Power-Reducing Formula is a powerful tool, it has limitations. It can only be used for trigonometric functions involving sine and cosine, and it may not work for all types of trigonometric expressions.

5. How can I apply the Power-Reducing Formula in my research or experiments?

The Power-Reducing Formula can be applied in a variety of scientific fields, such as physics, engineering, and astronomy. It can be used to solve problems involving periodic motion, oscillations, and wave phenomena.

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