В треугольнике ABC сторона АС 12 cm , угол А равен \( 45^{\circ} \), угол В равен \( 30^{\circ} \) Найдите сторону ВС.

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.

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

(d) Quando fazemos determinaçōes experimentais de uma grandeza \( X \), representamos seu valor numérico final acompanhado do erro \( \Delta X \) associado à medida, na forma \( X \pm \Delta X \). Para calcularmos o valor de uma funçāo \( f(X \pm \Delta X) \), utilizamos a regra \[ f(X \pm \Delta X)=f(X) \pm f^{\prime}(X) \Delta X \] Obtenha as fórmulas referentes a (i) \( \sin (X \pm \Delta X) \) e (ii) \( \cos (X \pm \Delta X) \)

When evaluating the expression \( \tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right) \), the angle obtained is ...

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