Question #93462

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Answer 1 · 2017-01-30T22:26:31

$tan(theta) = 5/3$
$sec(theta) = -sqrt(34)/3$
$cos(theta) = -(3sqrt(34))/34$
$sin(theta) = -(5sqrt(34))/34$
$csc(theta) = -sqrt(34)/5$

Given: $cot(theta) = 3/5 and sec(theta) < 0$

Use the identity $tan (theta) = 1/cot(theta)$ :

$tan(theta) = 1/(3/5)$

$tan(theta) = 5/3$

Use the identity $1 + tan^2(theta) = sec^2(theta)$

$1 + (5/3)^2 = sec^2(theta)$

$sec^2(theta) = 34/9$

$sec(theta) = -sqrt(34)/3$

Use the identity $cos(theta) = 1/sec(theta)$

$cos(theta) = -3/sqrt(34)$

$cos(theta) = -(3sqrt(34))/34$

Use the identity $tan(theta) = sin(theta)/cos(theta)$

$tan(theta)cos(theta) = sin(theta)$

$sin(theta) = 5/3(-(3sqrt(34))/34)$

$sin(theta) = (-5sqrt(34))/34$

Use the identity $csc(theta) = 1/sin(theta)$

$csc(theta) = 1/(-5/sqrt(34)$

$csc(theta) = -sqrt(34)/5$