This quiz covers sections 5.1 to 5.3 . The allowable time is 90 minutes. 1 Multiple Choice 1 point Find the exact value of \( \tan 2 \theta \), given that \( \cos \theta=-\frac{\sqrt{5}}{5}, \sin \theta>0 \). \( \frac{3}{5} \)

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

d) \( \frac{\sin \theta}{1-\cos \theta}-\frac{1+\cos \theta}{\sin \theta}=0 \quad \checkmark \checkmark \checkmark \checkmark \checkmark \)

5. Si \( \operatorname{sen} \theta=\frac{3}{5} \) determina el valor de \( M=3 \operatorname{tg} \theta \) \( \begin{array}{lll}\text { a. } \frac{3}{4} & \text { b. } 7 \frac{3}{4} & \text { c. } \frac{9}{4} \\ \text { d. } 1 \frac{3}{4} & \text { e. } \frac{35}{4} & \end{array} \)

c) \( \frac{\sin ^{2} \theta-3 \sin \theta+2}{\sin ^{2} \theta-1}=\frac{\sin \theta-2}{\sin \theta+1} \)

b) \( \csc \theta=\frac{\cos ^{2} \theta+\sin ^{2} \theta}{\sin \theta} \)