Given that \( \tan \phi=4 \), find the other frigonometric functions. \( \sin \phi=\frac{4 \sqrt{17}}{17} \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the express \( \cos \phi=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the express

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

1. Para hallar la distancia entre dos puntos \( A \) y \( B \) que se encuentran en margenes opuestos de un río, un topógrafo traza un segmento de recta \( A C \) de 240 metros de longitud a lo largo de uno de los márgenes y determina las me- didas del \( \angle B A C=63^{\circ} \) y \( \angle A C B=54^{\circ} \). Calculi la distancia entre \( A \) y \( B \).

3. Prove \( \sin 3 x=3 \cos ^{2} x \sin x-\sin ^{2} x \) 4. Prove \( \sec 2 x=\frac{\csc ^{2} x}{\csc ^{2} x-2} \) 5. Prove \( \frac{1+\cos \theta}{\sin \theta}+\frac{\sin \theta}{1+\cos \theta}=2 \csc \theta \) 6. Prove \( \frac{c s c^{2} \theta-1}{c s^{2} \theta}=\cos ^{2} \theta \) 7. Prove \( \frac{1}{1-\cos ^{2}}+\frac{1}{1+\cos \mathrm{B}}=2 \csc ^{2} \) 8. Prove \( \left(\cot ^{2} A+1\right)\left(\sin ^{2} A-1\right)=-\cot ^{2} A \)

Which angle is coterminal with \( 170^{\circ} \) ? \( -190^{\circ}-450^{\circ}-350^{\circ} \)

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