Question 1 Find the lengths of the missing sides if side \( a \) is opposite angle A , side b is opposite angle B , and side c is the hypotenus \( \begin{array}{l}A=\frac{5}{12}, b=6\end{array} \)

5. Se observa un semáforo desde la ventana de un edificio, a 30 m del suelo. El ángulo de depresión para observar la parte superior del semáforo es de \( 70^{\circ} \), mientras que el ángulo de depresión para observar su base mide \( 88^{\circ} \). ¿Cuál es la altura del semáforo?

Prove the following trigonometric identity: \( \frac{\sin A\left[1-\sin \left(360^{\circ}-A\right)\right]}{1-\cos ^{2}\left(180^{\circ}+A\right)}-1=\operatorname{cosec} A \)

8. The teminal amm for angle \( \theta \) passes through the point \( (7,-6) \). a) Determine the exact simplified ralues of the 6 trigonometric ratios, inolube a diagram.

The displacement, \( d \), in millimeters of a tuning fork as a function of time, \( t \), in seconds can be modeled with the equation \( d=0.4 \sin (1760 \pi f) \). What is the maximum displacement of the tuning fork? 0.2 mm 0.4 mm 0.8 mm 2.5 mm

What is the period of \( y=\sin (3 x) \) ? \( \begin{array}{l}\frac{\pi}{3} \\ \frac{2 \pi}{3} \\ 3 \pi \\ 6 \pi\end{array} \)