Trigonometry

Calisia McLean

Trigonomic functions

The trigonometric functions are among the most fundamental in mathematics. The significance of applied mathematics extends beyond basic uses, because they can be used to describe any natural phenomenon that is periodic, and in higher mathematics they are fundamental tools for understanding many abstract spaces.

Trig functions cont.The Unit Circle-

Trig Functions cont.

The primary use of trigonometric functions is in the measurement of angles.

The trigonometric functions are most easily understood in the context of a circle in the Cartesian plane.

For example: sin=y/r

Abraham de MoivreMay 26, 1667 ~ November 27, 1754

•French-born mathematician who pioneered the development of analytic geometry and the theory of probability.

•Was influenced in mathematics because of the work of Newton’s Principia.

•Created imaginary quantities with Lambert

•First to express Trig functions using a system of algebra

•Nth power of an expression involving trig functions and the imaginary unit i.[r(cos

•Began the analytic side of Trig.

Trigonometry In The Real World

• Why do I have to learn trigonometry? Where will I ever use this in real life?

• The answers usually involve Engineering such as finding heights of buildings, surveying, stock market, or business cycles.

• Example: Kent, a business owner who creates and sells metal sculptures is looking for the dimensions required to make a three-dimensional, five pointed star.

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Sinusoidal Function

• Basically sinusoids are graphs of wave forms, having periodic behavior or wave characteristics that can be represented by trigonometric functions or (approximately) modeled by sinusoids. This includes many simple actions such as a pendulum, a child's swing, motion of an engine's piston-crankshaft, a Ferris wheel, tides, blood pressure in the heart, hours of daylight through out a year, (visible) shape of the moon, seasons, and sounds.

Sinusoidal Cont.

One Example of Sinusoidal is a person’s biorhythm. Proponents of biorhythms claim our daily lives are significantly affected by rhythmic cycles and that these cycles can interact to indicate active and passive phases in the physical, emotional and mental aspects of humans.

A Ferris Wheel A Ferris wheel appears in a common textbook problem involving sinusoids where students are asked to determine the height of a rider above the ground. As they simulate the rotation of the wheel a sinusoid is generated as a plot of the angle of rotation from the vertical vs. the height of a (particular) car above the ground.