Trigonometry

Trig Identity:

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Converting between Degrees-minutes-seconds and degrees

1 degree = 60 minutes 1 minute = 60 seconds 1 minute = 1/60 degrees 1 second = 1/3600 degrees

Common Trigonometric Ratios

3,4,5

Unit Circle

A special circle with the radius of 1. These are the ones where the (x,y) coordinates along the circle are easy to fine.

Why do we use trig?

Anything that uses a triangle or a wave Astronomy - where will the heavenly body be? Geometry Optics Architecture Seasonal Phenomena (weather) Signal Processing

Inverse Trig Functions

Cosecant, secant, cotangent

Graphs of Trig Functions

Each function has a characteristic period - the amount of time until it repeats again.

One rotation around the unit circle

Measures 2 pi radians because the radius is 1 so the circumference is 2 pi r

Trigonometric Functions

SOH CAH TOA (sine is opposite over hypotenuse, etc.)

Reference Angle

The acute positive angle formed by the terminal side of theta and the x axis.

Trigonometric Values of Special Angles (cos)

The cos of an angle is the x coordinate of the point of intersection of the point of intersection of the terminal side of the angle and the unit circle

Degrees and Radians

The radian measurement is the measure of the arc of the circumference covered by the angle

Trigonometry - means triangle measure

The relationships between sides and angles of triangles - in particular right triangles. We study triangle and circles. We study oscillatory behavior in a graph.

Trigonometric Values of Special Angles (sin)

The sin of an angle is equal to the y coordinate of the point of intersection of the terminal side of the angle intersects the unit circle

Coterminal Angles

They must share the same initial and terminal sides. Be really careful if they are asking you for a positive angle or a negative angle.