Chapter 6.3, Problem 75E

DISCUSS ■ DISCOVER: Viète’s Trigonometric Diagram In the 16th century the French mathematician François Viète (see page 50) published the following remarkable diagram. Each of the six trigonometric functions of θ is equal to the length of a line segment in the figure. For instance, sin θ = | PR|, since from ΔOPR we see that

$\sin \theta =\frac{\text{opp}}{\text{hyp}}=\frac{\left|PR\right|}{\left|OR\right|}=\frac{\left|PR\right|}{1}=\left|PR\right|$

For each of the live other trigonometric functions, find a line segment in the figure whose length equals the value of the function at θ. [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.]