MS 101 Alg & Trig test five • 03 July 2015 • Name:

1. The diagram above depicts the sinusoidal wave present in the wake behind the USNS Millinocket JHSV-3 when the ship is underway at sea.
   1. _____ About how many wavelengths are present in the wake wave behind the Millinocket?
   2. λ = _______________ What is the wavelength λ of the wake wave?
   3. a = _______________ What is the amplitude a of the wake wave?
   4. b = _______________ Given that $b=\frac{2\pi }{\lambda }$, calculate the value of b for the wake wave.
   5. y = ______ sin( _________ x). Given the general form y = a sin(bx) and the results above, write the y = a sin(bx) equation for run A.
2. 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.
3. Explain what happens and why to the graph of the function y = tan(x) for x = -90° and x = 90°
4. Calculate the values of θ = ______________ and φ = ______________.
   
5. 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.
   
6. 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 = _______ Calculate the angle θ in degrees
   2. φ = _______ Calculate the angle φ in degrees
   3. r = _______ Calculate the length of the hypotenuse in kilometers