course mth 164 }`\Zzassignment #006
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19:30:02 Query problem 6.5.10 exact value of sin^-1( -`sqrt(3)/2)
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RESPONSE --> confidence assessment:
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19:30:15 Query problem 6.5.10 exact value of sin^-1( -`sqrt(3)/2)
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RESPONSE --> -pi/3 confidence assessment: 3
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Lɭzdƾؗ_ assignment #006 006. Precalculus II 06-15-2007
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19:31:04 Query problem 6.5.10 exact value of sin^-1( -`sqrt(3)/2)
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RESPONSE --> The answer would be -pi/3 confidence assessment: 3
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19:31:18 what is the exact value of the given expression?
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RESPONSE --> The exact value is -pi/3 confidence assessment: 3
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19:33:42 Describe the triangle you would use to evaluate this expression, and explain how you would use it.
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RESPONSE --> I would use a 30, 60, 90 triangle to solve this problem The 60 degree angle would be at the origin, hypotenuse 1 and drop a perpendicular to the x-axis to form a right triangle confidence assessment: 2
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19:35:05 Query problem 6.5.34 exact value of cos(sin^-1(-`sqrt(3 / 2 ))?
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RESPONSE --> since in the previous problem it was found that sin^1(-sqrt(3)/2)) is -pi/3 then we would find cos(-pi/3) which is equal to 1/2 confidence assessment: 3
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19:35:16 what is the exact value of the given expression?
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RESPONSE --> The exact value is 1/2 confidence assessment: 3
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19:36:27 Describe the triangle you would use to evaluate this expression, and explain how you would use it.
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RESPONSE --> I would use the same triangle as before to find the value of sin^1(-sqrt(3)/2)) and then the cos of that angle would be the x coordinat of the vertex of the triangle on the unit circle confidence assessment: 2
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19:37:17 Query problem 6.5.88 cos(tan^-1(v)) = 1 / `sqrt(1+v^2)
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RESPONSE --> ok confidence assessment: 3
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19:39:13 explain how you establish the given identity.
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RESPONSE --> First set up a right triangle and identify one angle as theta. Since tangent is opposite/adjacent then the opposite leg would be v and the adjacent leg would be 1. Using the pythagorean theorem the hypotenuse would be sqrt(1+v^2). Using the trig ratio for cosine which is adjacent over hypotenuse we find that the cosine of that angle would be 1/sqrt(1+v^2) confidence assessment: 3
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19:39:27 Describe the triangle you might use to establish this identity and how you would use it.
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RESPONSE --> I described it in the answer before. confidence assessment: 3
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19:40:20 Comm on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> Right triangles can be used for a wide range of purposes not just for finding the length of sides from two sides but also from trig ratios not even knowing the measure of the angle. confidence assessment: 3
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