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Q:

# What are some examples using sinusoidal functions in real life?

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In the real world, sinusoidal functions can be used to describe mechanical functions such as the swinging of a pendulum or natural phenomena such as hours of daylight. Sinusoidal functions graph wave forms.

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As such, sinusoidal functions can be used to describe any phenomenon that displays a wave or wave-like pattern or by extension any predictable periodic behavior. They are applicable in many real life cases.

• The periodic rotations of a crankshaft in an engine
• The rotation of a Ferris wheel
• The fluctuating hours of daylight in a specific location throughout a calendar year
• Fluctuating use of energy to heat a home through the seasons.
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## Related Questions

• A:

When it is three o’clock, the two hands of the clock are on digits 12 and 3. The seconds hand moves between these two digits and forms a pair of complementary angles in real life. The sum of the two angles formed by the seconds hand is always 90 degrees.

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• A:

Parent functions are the unmodified form of a family of functions, and parent functions must preserve the shape of the family graph. Modifications to the parent function are transformations. Adding, subtracting, multiplying or dividing by a real number causes a transformation, thus moving or modifying the parent function graph. Parent functions often undergo several transformations.

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The periods of the trigonometric functions sine and cosine are both 2 times pi. The functions tangent and cotangent both have a period of pi. The general formula for the period of a trigonometric function can be determined by dividing the regular period by the absolute value of any multipliers.