Unit-6 Trigonometry and Bearing
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Unit-6 Trigonometry and Bearing
Answer: cot theta = 1 / tan theta = cos theta / sin theta.
Answer: sin 60 = sqrt 3 / 2.
Answer: cot 45 = 1 / tan 45 = 1 / 1 = 1.
Answer: cos 90 = 0, so tan 90 = sin 90 / cos 90 is undefined.
Answer: cot = adjacent/opposite = 5/12 gives hypotenuse 13, so sin theta = 12/13 and csc theta = 13/12.
Answer: 315 degrees clockwise from North is North-West.
Answer: cos theta = adjacent / hypotenuse = 4/5.
Answer: Dividing sin^2 theta + cos^2 theta = 1 by cos^2 theta gives 1 + tan^2 theta = sec^2 theta.
Answer: csc theta = 1 / sin theta = 1 / (3/5) = 5/3.
Answer: (1 / sqrt 2)^2 + (1 / sqrt 2)^2 = 1/2 + 1/2 = 1.
Answer: South is 180 degrees clockwise from North.
Answer: One complete revolution around a point equals 360 degrees.
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Answer: tan theta = height / shadow = 1, so theta = 45 degrees.
Answer: sec theta = 1 / cos theta.
Answer: 1 - sin^2 theta = cos^2 theta, so cos^2 theta / cos theta = cos theta.
Answer: sin theta = opposite / hypotenuse = 3/5.
Answer: 135 degrees clockwise from North points to South-East.
Answer: cos 30 = sqrt 3 / 2.
Answer: sin 45 = 1 / sqrt 2 = sqrt 2 / 2.
Answer: (2 pi/3) x (180/pi) = 120 degrees.