Chapter 1: Understanding Sine Waves

Life mirrors the rhythm of a sine wave, characterized by its peaks and troughs, flowing endlessly in cycles. Today’s challenge invites you to delve into the sine curve and gauge your knowledge of trigonometry.

Don't let the seemingly daunting angles discourage you! Once you recognize the underlying pattern, a moment of clarity will dawn upon you.

I encourage you to take a moment, grab your pen and paper, and attempt the puzzle. Once you're prepared, continue reading for the solution!

Section 1.1: Exploring the Puzzle

When faced with numerous terms, it’s wise to begin by analyzing the initial terms. Let’s examine them below:

To derive their values, we can refer to the sine curve:

From our observations, the values correspond to 1, 0, -1, and 0 sequentially. Thus, we compute:

1 + 0 - 1 + 0 = 0

Now, let’s consider the other terms leading up to sin(3600°):

Given that 3600° divided by 360° equals 10, we see that the sum encompasses 10 complete cycles of the sine wave.

This indicates that the total sum is 0 multiplied by 10, equating to 0—there’s our answer!

Isn’t that remarkable?

What was your thought process during this exercise? Please share in the comments; I’m keen to hear your insights!

Chapter 2: Engage with More Math Challenges

Explore and share a list of intriguing math puzzles available on Medium, encompassing topics from Algebra to Calculus.

Stay tuned for Bella’s Weekly Math Games, featuring a 48-hour math competition every week!

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Happy Solving, Bella!

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