SOLUTION: For the following, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270° < A < 360°.
If sin B = − 1/5 with B in QIII, find
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-> SOLUTION: For the following, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270° < A < 360°.
If sin B = − 1/5 with B in QIII, find
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Question 740819: For the following, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270° < A < 360°.
If sin B = − 1/5 with B in QIII, find the following.cot B/2
You can put this solution on YOUR website! If sin B = − 1/5 with B in QIII, find the following.
cot(B/2) = 1/tan(B/2) = (1 + sqrt(1+tan^2(B))/tan(B)
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Since sin(B) = -1/5, y = -1 and r = 5
Then x = sqrt(r^2-y^2) = sqrt(25-1) = sqrt(24)
Note: x is negative in QIII
So x = -sqrt(24)
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Therefore tan(B) = y/x = -1/-sqrt(24) = 1/sqrt(24)
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Finally, cot(B/2) = (1 + sqrt(1+(1/24))/[1/sqrt(24)]
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= (1+sqrt(25/24))*(sqrt(24))
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= (1+5/(sqrt(24))(sqrt(24)
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= sqrt(24)+5
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Cheers,
Stan H.
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