Chapter 5.3, Problem 75E

DISCUSS DISCOVER PROVE WRITE

DISCUSS ■ DISCOVER: Viète’s Trigonometric Diagram In the $16th$ century the French mathematician François Viète (see page $119)$ published the following remarkable diagram. Each of the six trigonometric functions of $\theta$ is equal to the length of a line segment in the figure. For instance, $\sin \theta =\left|PR\right|,$ since from $△OPR$ we see that $\sin \theta =\frac{opp}{hyp}=\frac{\left|PR\right|}{\left|OR\right|}=\frac{\left|PR\right|}{1}=\left|PR\right|$ For each of five other trigonometric functions, find a line segment in the figure whose length equals the value of the function at $\theta .$ [Note: The radius of the circle is $1,$ the center is $O,$ segment $QS$ is tangent to the circle at $R,$ and $\angle SOQ$ is a right angle.]