Credit:Dave FayramCC-BY-SA 2.0

Q: A: ### Quick Answer

**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.

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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## What are complementary angles in real life?

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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## What does cosine mean?

A:The cosine function is one of the three basic functions used in trigonometry. The cosine of a right triangle is found by taking the ratio of the length of the triangle's adjacent side over the length of the hypotenuse. In other words, divide them.

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## What is the period of some trig functions?

A: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.

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## How do you find the derivative of sin2x?

A:To find the derivative of a sin(2x) function, you must be familiar with derivatives of trigonometric functions and the chain rule for finding derivatives. You need scratch paper and can use a graphing calculator to check coordinates and slopes at specific values.

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