Reciprocal Trigonometric Functions - Virtual Math Learning Center

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.

Concepts

Defining the reciprocal trigonometric ratios cosecant, secant, and tangent

Watch: Recipricol Trig Functions

Exercises

Directions: You should attempt to solve the problems first and then watch the video to see the solution.

1. Find the ratios \(\csc{\theta}, \sec{\theta}\) and \(\cot{\theta}\) in the given triangle.

A right triangle with legs of 6 and square root 2, hypotenuse of 2 time square root of 10, and angle theta opposite the square root 2 side

A right triangle with legs of 6 and square root 2, hypotenuse of 2 time square root of 10, and angle theta opposite the square root 2 side

Reveal Answer

\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*}

2. Given a right triangle with \(\sin{\phi} = \frac{12}{37}\) and \(\sec{\phi}= \frac{37}{35}\), find the remaining 4 trigonometric ratios.

Reveal Answer

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Solving Problems With Trig

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