Unit-6 Trigonometry and Bearing
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Unit-6 Trigonometry and Bearing
Answer: sec 0 = 1 / cos 0 = 1 / 1 = 1.
Answer: cos 60 = 1/2.
Answer: (5 pi/6) x (180/pi) = 150 degrees.
Answer: 30 = 180/6, so 30 degrees = pi/6 radians.
Answer: cos theta = 1 / sec theta = 1/2.
Answer: 75 x (pi/180) = 75 pi / 180 = 5 pi / 12.
Answer: sin theta = 1 / csc theta = 1/2.
Answer: sin 30 = opposite / 10, so opposite = 10 x (1/2) = 5.
Answer: sin 0 = 0.
Answer: 120 x (pi/180) = 120 pi / 180 = 2 pi / 3.
Answer: 0.5 degree = 0.5 x 60 = 30 minutes.
Answer: (pi/2) x (180/pi) = 90 degrees.
Answer: A right angle is one-quarter of a full revolution, which equals 90 degrees.
Answer: In the sexagesimal system, 1 degree = 60 minutes (60').
Answer: The Pythagorean identity states sin^2 theta + cos^2 theta = 1.
Answer: 60 = 180/3, so 60 degrees = pi/3 radians.
Answer: csc 90 = 1 / sin 90 = 1 / 1 = 1.
Answer: tan theta = East/North = 4/3, so theta = arctan(4/3) approx 53.13 degrees clockwise from North.
Answer: cos theta = sqrt(1 - sin^2 theta) = sqrt(1 - 9/25) = sqrt(16/25) = 4/5.
Answer: 45' + 30' = 75' = 1 degree 15'; the total is 51 degrees 15 minutes.