Find \( \cos \theta \) if the \( y \)-coordinate of the point where the terminal side of \( \theta \) intersects the unit circ is \( \frac{\sqrt{2}}{2} \), given that \( \theta \) is an acute angle and in the first quadrant. (1 point) \( \cos \theta= \)

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 \( B \).

4 ¿Cuál es el valor del ángulo absoluto del vector? (Escriba solo el valor, sin la unidad \( { }^{\circ} \) ) * \( \vec{b}=6.8 \mathrm{Km}, 83^{\circ} \) al SOe

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 \( c=\frac{3}{2} \).

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

\( \left. \begin{array} { l }{ 40 ^ { \circ } 12 ^ { \prime } 48 ^ { \prime \prime } } \\ { + 17 ^ { \circ } \quad 5 ^ { \prime } 59 ^ { \prime \prime } } \end{array} \right. \)