Six Trigonometric Functions

Trigonometry Mnemonic

Sohcahtoa, the Indian princess of Trigonometry

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

Basic Trigonometry Videos:

Basic Trigonometry : Introduction to trigonometry

Basic Trigonometry II: A few more examples using SOH CAH TOA

Radians and degrees : What a radian is. Converting radians to degrees and vice versa.

Using Trig Functions : Using Trigonometric functions to solve the sides of a right triangle

Using Trig Functions Part II

The unit circle definition of trigonometric function

Unit Circle Definition of Trig Functions


Definition I
If θ is an angle in standard position, and the point (x,y) is any point on the terminal side of θ other than the origin, then the six trigonometric functions of angle θ are defined as follows:

Function            Abbreviation                  Definition      
The sine of θ         = sin θ      = y/r
The cosine of θ    = cos θ      = x/r
The tangent of θ    = tan θ      = y/x (x ≠ 0)
The cotangent of θ            = cot θ      = x/y (y ≠ 0)
The secant of θ    = sec θ      = r/x (x ≠ 0)
The cosecant of θ    = csc θ      = r/y (y ≠ 0)

where x2 + y2 = r2, or r = √x2 + y2.>
That is, r is the distance from the origin to (x,y)


The symbol θ is called “theta” (pronouced ‘thayta’).
Theta ( θ )  is the eighth letter in the greek alphabet and is used in trigonometry as a representation of an angle measurement.


McKeague, C. and Turner, M. (2008). Trigonometry (6th ed.). Belmont, CA: Brooks/Cole, Cengage Learning

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