Online Math Tutor LLC

Discover the Path to Mathematical Mastery 
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Online Math Tutor LLC

Discover the Path to Mathematical Mastery 
An Education That Counts

Trigonometric Basics

Definitions and relationships of the six fundamental trigonometric functions.

SOCATOA

\(\displaystyle \texttt{sin}(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \)
\(\displaystyle \texttt{cos}(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \)
\(\displaystyle \texttt{tan}(\theta) = \frac{\text{opposite}}{\text{adjacent}} \)
\(\displaystyle \texttt{csc}(\theta) = \frac{\text{adj}}{\text{opp}} \)
\(\displaystyle \texttt{sec}(\theta) = \frac{\text{adj}}{\text{hyp}} \)
\(\displaystyle \texttt{tan}(\theta) = \frac{\text{opp}}{\text{adj}} \)
\(\displaystyle \texttt{csc}(\theta) = \frac{\text{hypotenuse}}{\text{opposite}} \)
\(\displaystyle \texttt{sec}(\theta) = \frac{\text{hypotenuse}}{\text{adjacent}} \)
\(\displaystyle \texttt{cot}(\theta) = \frac{\text{adjacent}}{\text{opposite}} \)
\(\displaystyle \texttt{csc}(\theta) = \frac{\text{hyp}}{\text{opp}} \)
\(\displaystyle \texttt{sec}(\theta) = \frac{\text{hyp}}{\text{adj}} \)
\(\displaystyle \texttt{cot}(\theta) = \frac{\text{adj}}{\text{opp}} \)

\(\big(\texttt{Adjacent}\big)^2+\big(\texttt{Opposite}\big)^2=\big(\texttt{Hypotenuse}\big)^2 \)

Circular Functions

\(\displaystyle \texttt{sin}(\theta) = \frac{y}{r} \)
\(\displaystyle \texttt{cos}(\theta) = \frac{x}{r} \)
\(\displaystyle \texttt{sin}(\theta) = \frac{y}{x} \)
\(\displaystyle \texttt{csc}(\theta) = \frac{y}{r} \)
\(\displaystyle \texttt{sec}(\theta) = \frac{x}{r} \)
\(\displaystyle \texttt{tan}(\theta) = \frac{y}{x} \)

\(x^2+y^2=r^2 \)

\(\big(\texttt{Adjacent}\big)^2+\big(\texttt{Opposite}\big)^2=\big(\texttt{Hypotenuse}\big)^2 \)