Find: \(\sin(\pi)\) and \(\cos(\pi)\)
Notes...
White Star Line • Flashcard 10 Crew
Lookout: Frederick Fleet
Into the cold dark of Quadrant III. Fleet spots an iceberg. Calculate the vertical coordinate of the sighting.
Find: \(\sin(210^\circ)\)
Notes...
White Star Line • Flashcard 11 Crew
Operator: Jack Phillips
Phillips sends an SOS. The distress signal travels at this angle. What is the slope of the signal path?
Find: \(\tan(\frac{5\pi}{4})\)
Notes...
White Star Line • Flashcard 12 Crew
Musician: Wallace Hartley
The band plays "Nearer, My God, to Thee". Calculate the horizontal coordinate at this angle in Quadrant III.
Find: \(\cos(240^\circ)\)
Notes...
White Star Line • Flashcard 13 Hull
Event: Ship Sinking
The stern rises and the ship heads due South toward the ocean floor. Find the cosine and sine values.
Find: \(\cos(\frac{3\pi}{2})\) and \(\sin(\frac{3\pi}{2})\)
Notes...
White Star Line • Flashcard 14 Rescue
Ship: RMS Carpathia
The Carpathia arrives from the Southeast (Quadrant IV) to rescue survivors. Find the slope of its path.
Find: \(\tan(300^\circ)\)
Notes...
White Star Line • Flashcard 15 Rescue
Port: New York City
The survivors finally reach New York. Calculate the vertical coordinate of the final destination on the unit circle.
Find: \(\sin(\frac{7\pi}{4})\)
Notes...
White Star Line • Flashcard 16 Legacy
Event: Legend of Titanic
The story comes full circle. Calculate the horizontal position just before completing the rotation.
Find: \(\cos(330^\circ)\)
Notes...
Confidential Answer Key for Instructors
Card 01 (\(0^\circ\)):
\(\sin(0) = 0\) | \(\cos(0) = 1\)
Card 02 (\(30^\circ\)):
\(\tan(30^\circ) = \frac{\sqrt{3}}{3}\)
Card 03 (\(45^\circ\)):
\(\sin(45^\circ) = \frac{\sqrt{2}}{2}\)
Card 04 (\(60^\circ\)):
\(\cos(60^\circ) = \frac{1}{2}\)
Card 05 (\(90^\circ\)):
\(\tan(90^\circ) = \text{Undefined}\)
Card 06 (\(120^\circ\)):
\(\sin(120^\circ) = \frac{\sqrt{3}}{2}\)
Card 07 (\(135^\circ\)):
\(\cos(135^\circ) = -\frac{\sqrt{2}}{2}\)
Card 08 (\(150^\circ\)):
\(\tan(150^\circ) = -\frac{\sqrt{3}}{3}\)
Card 09 (\(180^\circ\)):
\(\sin(\pi) = 0\) | \(\cos(\pi) = -1\)
Card 10 (\(210^\circ\)):
\(\sin(210^\circ) = -\frac{1}{2}\)
Card 11 (\(225^\circ\)):
\(\tan(225^\circ) = 1\)
Card 12 (\(240^\circ\)):
\(\cos(240^\circ) = -\frac{1}{2}\)
Card 13 (\(270^\circ\)):
\(\cos(270^\circ) = 0\) | \(\sin(270^\circ) = -1\)
Card 14 (\(300^\circ\)):
\(\tan(300^\circ) = -\sqrt{3}\)
Card 15 (\(315^\circ\)):
\(\sin(315^\circ) = -\frac{\sqrt{2}}{2}\)
Card 16 (\(330^\circ\)):
\(\cos(330^\circ) = \frac{\sqrt{3}}{2}\)
© 1912 White Star Line Navigation Department
Passenger: Ida Straus
"Where you go, I go." Ida stays with her husband. Calculate the slope (tangent) of their united path.
Find: \(\tan(\frac{4\pi}{3})\)
Notes...
White Star Line • Flashcard 26 1st Class
Passenger: Isidor Straus
The owner of Macy's refuses to board a boat before other men. Find his vertical position in Quadrant IV.
Find: \(\sin(\frac{5\pi}{3})\)
Notes...
White Star Line • Flashcard 27 1st Class
Passenger: Madeleine Astor
The pregnant wife of J.J. Astor survives the night. Calculate the horizontal coordinate (cosine) of her position.
Find: \(\cos(\frac{7\pi}{4})\)
Notes...
White Star Line • Flashcard 28 2nd Class
Passenger: Eva Hart
A child survivor who remembered the ship's lights going out. Find the slope (tangent) of this final radian angle.
Find: \(\tan(\frac{11\pi}{6})\)
Notes...
White Star Line • Flashcard 29 Depths
Location: The Wreckage Site
The ship rests on the ocean floor. Calculate the coordinates of this negative coterminal heading.
Find: \(\sin(-\frac{\pi}{4})\) and \(\cos(-\frac{\pi}{4})\)
Notes...
White Star Line • Flashcard 30 Legacy
Event: 100th Anniversary
The circle is complete. History remembers. Find the sine, cosine, and tangent of a full rotation.
Find: \(\sin(2\pi), \cos(2\pi), \tan(2\pi)\)
Notes...
Confidential Answer Key (Cards 17-30)
Card 17 (\(\pi/6\)):
\(\sin(\pi/6) = 1/2\)
Card 18 (\(\pi/4\)):
\(\cos(\pi/4) = \sqrt{2}/2\)
Card 19 (\(\pi/3\)):
\(\tan(\pi/3) = \sqrt{3}\)
Card 20 (\(2\pi/3\)):
\(\sin(2\pi/3) = \sqrt{3}/2\)
Card 21 (\(3\pi/4\)):
\(\cos(3\pi/4) = -\sqrt{2}/2\)
Card 22 (\(5\pi/6\)):
\(\tan(5\pi/6) = -\sqrt{3}/3\)
Card 23 (\(7\pi/6\)):
\(\sin(7\pi/6) = -1/2\)
Card 24 (\(5\pi/4\)):
\(\cos(5\pi/4) = -\sqrt{2}/2\)
Card 25 (\(4\pi/3\)):
\(\tan(4\pi/3) = \sqrt{3}\)
Card 26 (\(5\pi/3\)):
\(\sin(5\pi/3) = -\sqrt{3}/2\)
Card 27 (\(7\pi/4\)):
\(\cos(7\pi/4) = \sqrt{2}/2\)
Card 28 (\(11\pi/6\)):
\(\tan(11\pi/6) = -\sqrt{3}/3\)
Card 29 (\(-\pi/4\)):
\(\sin = -\sqrt{2}/2, \cos = \sqrt{2}/2\)
Card 30 (\(2\pi\)):
\(\sin=0, \cos=1, \tan=0\)
© 1912 White Star Line Navigation Department
