MS 101 Alg & Trig test five • 04 July 2014 Name:

Wave equation in terms of wavelength λ and distance x: $y=\mathrm{a}sin\left(\frac{2\mathrm{\pi }x}{\mathrm{\lambda }}\right)$
Wave equation in terms of period τ and time t: $y=\mathrm{a}sin\left(\frac{2\mathrm{\pi }t}{\mathrm{\tau }}\right)$
Period τ and frequency f relationship: $\mathrm{\tau }=\frac{1}{f}$

1. A RipStik lays down a wave according to the equation: $y=12sin\left(\frac{2\mathrm{\pi }x}{36}\right)$
   1. a = _______________ Write the amplitude a of the equation.
   2. λ = _______________ Write the wavelength λ of the equation.
2. A spring oscillates vertically according to the equation: $y=30sin\left(\frac{2\mathrm{\pi }t}{2.5}\right)$
   1. a = _______________ Write the amplitude a of the equation.
   2. τ = _______________ Write the period τ of the equation.
   3. f = _______________ Calculate the frequency f of the equation.
3. A RipStik was swizzled across a large sheet of paper. The swizzle wave can be seen in the diagram.
   
   1. ________ How many waves are shown in the diagram?
   2. λ = _______________ Write the wavelength λ
   3. a = _______________ Write the amplitude a.
   4. τ = _______________ Write the period τ.
   5. f = _______________ Calculate the frequency f.
   6. y = ______ sin( _________ x). Write out the equation of the wave in terms of the wavelength λ and distance x.
4. A Turkish F-4 Phantom II RC-4 is flying 23 kilometers off the coast of Syria. An anti-aircraft turret on the Syrian coast is tracking the Phantom.
   1. Write the equation for the angle θ as a function of the distance x along the coast and the distance (23) of the Phantom from the shore.
      θ =
   2. θ = _______ Calculate θ in degrees when x = 10.
5. Solve −4(cos x)² −3 = 0 for x in degrees
6. Sketch a graph of the following function: $y=40sin\left(\frac{2\mathrm{\pi }x}{4}\right)$
   
7. θ = __________ In the movie Pacific Rim the 260 foot tall Jaeger robot Gipsy Danger dragged a ship at an average angle θ as seen in the diagram. Calculate the angle θ in degrees.
   
8. Malaysian Airlines flight 370 disappeared on a flight from Kuala Lumpur to Beijing. Boats working in the area where the plane was thought to have crashed detected what was initially thought to be electronic signals from the submerged aircraft. A diagram is seen below.
   
   1. θ = _______ Use the information provided in the diagram to calculate the angle θ in degrees
   2. φ = _______ Use the information provided in the diagram to calculate the angle φ in degrees
   3. r = _______ Use the information provided in the diagram to calculate the length of the hypotenuse in kilometers