Unit-6 Trigonometry and Bearing
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Unit-6 Trigonometry and Bearing
Answer: From 1 + tan^2 theta = sec^2 theta, sec^2 60 - tan^2 60 = 1.
Answer: sin theta = side opposite theta divided by the hypotenuse.
Answer: tan 45 = 1 and tan 30 = 1 / sqrt 3, so the sum is 1 + 1 / sqrt 3.
Answer: tan 30 = 100 / d, so d = 100 / (1 / sqrt 3) = 100 sqrt 3 m.
Answer: 15/60 = 0.25, so 40 degrees 15' = 40.25 degrees.
Answer: tan 45 = sin 45 / cos 45 = 1.
Answer: tan = opposite/adjacent = 3/4 gives hypotenuse 5, so sin theta = 3/5.
Answer: (pi/3) x (180/pi) = 60 degrees.
Answer: Bearings are always measured clockwise from North.
Answer: sin 30 + cos 60 = 1/2 + 1/2 = 1.
Answer: The adjacent side is 4 and the hypotenuse is 5, so cos theta = 4/5.
Answer: Dividing sin^2 theta + cos^2 theta = 1 by sin^2 theta gives 1 + cot^2 theta = csc^2 theta.
Answer: 1 minute = 60 seconds of angle, since 1 degree = 3600 seconds.
Answer: By definition, a straight angle of 180 degrees equals pi radians.
Answer: cos 90 = 0.
Answer: cot 30 = 1 / tan 30 = sqrt 3.
Answer: 150 x (pi/180) = 150 pi / 180 = 5 pi / 6.
Answer: tan theta = opposite / adjacent = 5/12.
Answer: sin 60 = cos 30 = sqrt 3 / 2, so the difference is 0.
Answer: 1 + tan^2 45 = 1 + 1 = 2.