91Ó°ÊÓ

What is the angle between the hour hand and the minute hand on a clock at \(4: 30 ?\)

Find exact expressions for the indicated quantities, given that $$ \cos \frac{\pi}{12}=\frac{\sqrt{2+\sqrt{3}}}{2} \text { and } \sin \frac{\pi}{8}=\frac{\sqrt{2-\sqrt{2}}}{2} $$ [These values for \(\cos \frac{\pi}{12}\) and \(\sin \frac{\pi}{8}\) will be derived.] $$ \sin \frac{17 \pi}{8} $$

What is the angle between the hour hand and the minute hand on a clock at \(7: 15 ?\)

For Exercises \(17-24,\) sketch the unit circle and the radius corresponding to the given angle. Include an arrow to show the direction in which the angle is measured from the positive horizontal axis. $$ \frac{1}{2} \text { radian } $$

Suppose \(-\frac{\pi}{2}<\theta<0\) and \(\tan \theta=-2 .\) Evaluate: (a) \(\cos \theta\) (b) \(\sin \theta\)

Find the four smallest positive numbers \(\theta\) such that \(\sin \theta=\frac{1}{2}\)

Suppose \(a=5\) and \(\tan v=\frac{3}{4}\). Evaluate (a) b (b) \(c\).

Suppose \(0<\theta<\frac{\pi}{2}\) and \(\cos \theta=\frac{1}{3}\). Evaluate: (a) \(\sec \theta\) (b) \(\csc \theta\) (c) \(\cot \theta\)

Find exact expressions for the indicated quantities, given that $$ \cos \frac{\pi}{12}=\frac{\sqrt{2+\sqrt{3}}}{2} \text { and } \sin \frac{\pi}{8}=\frac{\sqrt{2-\sqrt{2}}}{2} $$ [These values for \(\cos \frac{\pi}{12}\) and \(\sin \frac{\pi}{8}\) will be derived.] $$ \tan \frac{25 \pi}{12} $$

What is the angle between the hour hand and the minute hand on a clock at \(1: 23 ?\)