Definitions

Trigonometric Functions

The Unit Circle

Radians and Degrees: Radians are the units of angles. Degrees are units of measurement of angles

Cosine: Adjacent side of triangle/ Hypotenuse side of triangle

Tangent: Opposite side of triangle/ Adjacent side of triangle

How to convert from one set of units to another:
-Write the conversion as a fraction
-Multiply
-Cancel any units that are both top and bottom

Terminal, co-terminal, and reference angles: Terminal side is a straight line that has been rotated around a point on another line to form an angle measured in a clockwise or counterclockwise direction. Co-terminal angles are angles who share the same initial side and terminal sides. Reference angles are the smallest angles between the terminal side and the x-axis.


The line where it says 30 degrees is the co-terminal angle. The reference angle is 30 degrees. The terminal side is 390 degrees.


https://i.imgsafe.org/0ab61d16bf.png

Cosecant: Reciprical of Sine

Positive and Negative angles: Negative angles are a way of measuring an angle from a different direction. A positive angle is created by rotating counter-clockwise around the origin of a coordinate system, starting at the x-axis (the horizontal axis) and proceeding through the quadrants in the order I, II, III, IV.

Secant: The Reciprocal of a Cosine.

Cotangent:Reciprocal of Tangent

Examples of radians and degrees:

Example of positive and negative angles:

The unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.

Sine: Opposite side of triangle/ Hypotenuse side of triangle

Trigonometric Functions: Degrees of the unit circle^

Trigonometric Functions: Radians of the unit circle^

45-45-90 triangle

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Real World example:

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Relationship map between 6 trig functions

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example of 6 trig functions for both 45-45-90 and
30-60-90

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