1007_Test1_Sol

1007_Test1_Sol - MATH 1007 A Test #1 September 29, 2006...

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MATH 1007 A Test #1 September 29, 2006 Solutions Angle 0 π/ 6 π/ 4 π/ 3 π/ 2 π sin x 0 1 / 2 1 / 2 3 / 2 1 0 cos x 1 3 / 2 1 / 2 1 / 2 0 - 1 tan x 0 1 / 3 1 3 n/a 0 Part A – Short Answer [16 marks] 1. [3 marks] Find cos ( 7 π 6 ) and sin ( 7 π 6 ) . Solution: cos ± 7 π 6 ² = cos ³ π + π 6 ´ = cos( π ) cos ³ π 6 ´ - sin( π ) sin ³ π 6 ´ = ( - 1) µ 3 2 ! - (0) ± 1 2 ² = - 3 2 sin ± 7 π 6 ² = sin ³ π + π 6 ´ = sin( π ) cos ³ π 6 ´ + cos( π ) sin ³ π 6 ´ = (0) µ 3 2 ! + ( - 1) ± 1 2 ² = - 1 2 1
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Find all values of x in the interval [0 , 2 π ] that satisfy 2 cos x - 1 = 0 . Solution: 2 cos x - 1 = 0 = 2 cos x = 1 = cos x = 1 2 = x = π 3 for 0 x π 2 The CAST rule tells us that the only other solution would be x = - π 3 , and converting this to a value between 0 and 2 π gives x = 2 π - π 3 = 5 π 3 . Hence there are 2 solutions, x = π 3 and x = 5 π 3 . 3. [3 marks] Let θ be an angle with cos θ = 5 6 . Draw a right-angled triangle with the angle θ and determine each of the 3 sides. Solution:
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1007_Test1_Sol - MATH 1007 A Test #1 September 29, 2006...

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