Find the Exact Values of the Six Trigonometric Functions of the Angle

question 359

Multiple Choice

Find the exact values of the six trigonometric functions of the angle $\theta$ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)

• A)sin \(\theta\) = \(\frac { 5 } { 3 }\) csc \(\theta\) = \(\frac { 3 } { 5 }\) cos \(\theta\) = \(\frac { 5 } { 4 }\) sec\(\theta\) = \(\frac { 4 } { 5 }\) tan\(\theta\) = \(\frac { 4 } { 3 }\) cot \(\theta\) = \(\frac { 3 } { 4 }\)
• B)sin \(\theta\)= \(\frac { 4 } { 3 }\) csc \(\theta\) = \(\frac { 3 } { 4 }\) cos\(\theta\) = \(\frac { 5 } { 4 }\) sec \(\theta\) = \(\frac { 4 } { 5 }\) tan \(\theta\) = \(\frac { 5 } { 3 }\) cot\(\theta\) = \(\frac { 3 } { 5 }\)
• C)sin \(\theta\) = \(\frac { 4 } { 5 }\) csc \(\theta\) = \(\frac { 3 } { 4 }\) cos \(\theta\) = \(\frac { 3 } { 5 }\) sec \(\theta\) = \(\frac { 4 } { 3 }\) tan\(\theta\) = \(\frac { 5 } { 3 }\) cot \(\theta\) = \(\frac { 5 } { 4 }\)
• D)sin \(\theta\) = \(\frac { 3 } { 5 }\) csc \(\theta\) = \(\frac { 5 } { 3 }\) cos \(\theta\) = \(\frac { 4 } { 5 }\) sec \(\theta\) = \(\frac { 5 } { 4 }\) tan \(\theta\) = \(\frac { 3 } { 4 }\) cot \(\theta\)= \(\frac { 4 } { 3 }\)
• E)sin \(\theta\) = \(\frac { 4 } { 3 }\) csc \(\theta\) = \(\frac { 5 } { 3 }\) cos \(\theta\) = \(\frac { 5 } { 4 }\) sec \(\theta\)= \(\frac { 3 } { 5 }\) tan \(\theta\)= \(\frac { 3 } { 4 }\) cot \(\theta\) = \(\frac { 4 } { 5 }\)

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Definitions:

The Swing

A famous Rococo painting by Jean-Honoré Fragonard, depicting a young woman swinging while being watched by her lover, embodying the playful and sensual style of the period.

Rococo

An 18th-century artistic movement and style, originating in France, characterized by elaborate ornamentation, asymmetrical values, pastel color palette, and themes of love, nature, and light-heartedness.

Fragonard

Jean-Honoré Fragonard was a French painter whose works are emblematic of the Rococo style, known for its playful, sensuous expression.

Jean-Jacques Rousseau

A Genevan philosopher, writer, and composer of the 18th century, whose ideas influenced the Enlightenment across Europe, as well as aspects of the French Revolution.