Reciprocal Trig Functions
Instructions
- The first videos below explain the concepts in this section.
- This page includes exercises that you should attempt to solve yourself and then check your answers.
- When you are done, you can use the graph to pick another section or use the buttons to go to the next section.
Learning Objectives
- Defining the reciprocal trigonometric ratios cosecant, secant, and tangent
Concept Video(s)
Exercises
1.
\begin{align*}
\csc{\theta} &= \frac{2\sqrt{10}}{\sqrt{2}} \\
&= \frac{2\sqrt{10 \cdot 2}}{2} \\
&= \sqrt{20} \\
&= 2\sqrt{5}\\[10pt]
\sec{\theta} &= \frac{2\sqrt{10}}{6} \\
&= \frac{\sqrt{10}}{3} \\[10pt]
\cot{\theta} &= \frac{6}{\sqrt{2}} \\
&= \frac{6\sqrt{2}}{2} \\
&= 3\sqrt{2}
\end{align*}
\csc{\theta} &= \frac{2\sqrt{10}}{\sqrt{2}} \\
&= \frac{2\sqrt{10 \cdot 2}}{2} \\
&= \sqrt{20} \\
&= 2\sqrt{5}\\[10pt]
\sec{\theta} &= \frac{2\sqrt{10}}{6} \\
&= \frac{\sqrt{10}}{3} \\[10pt]
\cot{\theta} &= \frac{6}{\sqrt{2}} \\
&= \frac{6\sqrt{2}}{2} \\
&= 3\sqrt{2}
\end{align*}
2.
\begin{align*}
\cos{\phi} &= \frac{35}{37} \\[8pt]
\tan{\phi} &= \frac{12}{35} \\[8pt]
\csc{\phi} &= \frac{37}{12} \\[8pt]
\cot{\phi} &= \frac{35}{12}
\end{align*}
\cos{\phi} &= \frac{35}{37} \\[8pt]
\tan{\phi} &= \frac{12}{35} \\[8pt]
\csc{\phi} &= \frac{37}{12} \\[8pt]
\cot{\phi} &= \frac{35}{12}
\end{align*}