Find the coordinates of the point shown on the unit circle, if \( \cos \theta=-\frac{1}{2} \). (1 point)

For what values of the angle between \( \vec{A} \) and \( \vec{B} \) will the dot product \( \vec{A} \vec{B} \) be positive, negative or zero?

\( \frac { \cos \theta + \cos \beta } { \sin \theta - \sin \beta } = \frac { \sin \theta + \sin \beta } { \cos \beta - \cos \theta } \)

4. Numeric 15 points \( \begin{array}{l}\text { 2. A construction worker leans his ladder } \\ \text { against a building making a } 60^{\circ} \text { angle with } \\ \text { the ground. If his ladder is } 20 \text { feet long, how } \\ \text { far away is the base of the ladder from the } \\ \text { building? Round to the nearest tenth. }\end{array} \) Type your answer...

Points \( A \) and \( B \) are separated by a lake. To find the distance between them, a surveyor locates a point \( C \) on land such than \( \angle C A B=51.4^{\circ} \). Find the distance across the lake from \( A \) to \( B \).

6 The graph \( y=a+b \cos (c x) \) is defined for \( 0 \leq x \leq 2 \pi \), where \( a, b \) and \( c \) ar constants. The graph has a period of \( \frac{4 \pi}{3} \) and a minimum value of 1 when \( x=\frac{4 \pi}{3} \). The graph also passes through the point \( \left(\frac{\pi}{3}, 3\right) \). (a) Show that \( a=3, b=-2 \) and \( c=\frac{3}{2} \).