Determine the quadrant when the terminal side of the angle lies according to the following conditions: \( \sin (t)>0 \), \( \sec (t)>0 \).

- \( \left|\begin{array}{l}\text { 1.Решите уравнение. В ответе напишите } \\ \text { наименьший положительный корень. } \\ \sin \frac{\pi(x+9)}{4}=-1\end{array}\right| \)

En el triángulo rectángulo \( A B C \) de la siguiente imagen, se cumple que \( \cos \beta=\frac{1}{2} \).

\begin{tabular}{|l|} 3. Решите уравнение. В ответе напишите \\ наибольший отрицательный корень. \\ \( \sin \frac{\pi(4 x+5)}{6}=-0,5 \)\end{tabular}

The angle of depression from one mountain summit to another is \( 15.9^{\circ} \). If the two mountains differ in height by 430 metres, find the horizontal distance between the two summits, to the nearest centimetre.

a) \( \sin ^{4} x+\cos ^{2} x \cdot \sin ^{2} x-\sin ^{2} x \)