4. The constants K and C for a certain instrument were 100 and 0 respectively. The ground makes a uniform slope of \( 12 \% \) from point A to point B . With the instrument at A and staff at B , readings were taken but due to obstruction in the line of sight, only the upper reading was recorded to be 1.915 m . If the vertical angle of the instrument was \( 6^{\circ} 43^{\prime} \) and height of instrument above A was 1.82 m , determine the horizontal distance between A and B .

Solve \( 8 \sin \left(\frac{\pi}{5} x\right)=4 \) for the four smallest positive solutions

Solve \( \sin ^{2}(t)=-8 \cos (t) \) for all solutions \( 0 \leq t<2 \pi \)

i) \( \frac{\tan \theta \cot \theta}{\sec \theta} \) equals: A \( \sin \theta \)

Given that \( \tan 75^{\circ}=2+\sqrt{3} \) hence determine \( \tan 15^{\circ} \) leaving your answer in the form \( a+b \sqrt{c} \)

Solve the equation for exact solutions over the interval \( [0,2 \pi) \) \( 2 \tan 3 x=2 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \left\{\frac{\pi}{12}, \frac{5 \pi}{12}, \frac{3 \pi}{4}, \frac{13 \pi}{12}, \frac{17 \pi}{12}, \frac{7 \pi}{4}\right\} \). (Type an exact answer, using \( \pi \) as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a com B. The solution is the empty set.