Using a unit circle, what is cos the angle \( \frac{-\pi}{6} \) ? \( \frac{\frac{\sqrt{2}}{2}}{\frac{-\sqrt{2}}{2}} \) \( \frac{-\sqrt{3}}{2} \) \( \frac{-1}{2} \)

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

The equation \( h=7 \sin \left(\frac{\pi}{21} t\right)+28 \) can be used to model the height, \( h \), in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, \( t \), in seconds. How long is the blade? Assume that the blade is pointing to the right, parallel to the ground, at \( t=0 \), and that the windmill turns counterclockwise at a constant rate. 7 feet 14 feet 21 feet 28 feet

Which transformations are needed to change the parent cosine function to \( y=3 \cos (10(x-\pi)) \) ? vertical compression of 3 , horizontal stretch to a period of \( 5 \pi \), phase shift of \( \pi \) units to the left vertical stretch of 3 , horizontal compression to a period of \( \frac{\pi}{5} \), phase shift of \( \pi \) units to the right vertical compression of 3 , horizontal stretch to a period of 10 p, phase shift of \( \pi \) units to the right vertrech of 3 , horizontal compression to a period of \( \frac{\pi}{5} \), phase shift of \( \pi \) units to the left

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

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?