How do you use $tantheta=4$ to find $csctheta$ ?

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Answer 1 · 2017-01-14T21:46:08

Use the identities $cot(theta)=1/tan(theta)$ and $csc(theta) = +-sqrt(1 + cot^2(theta))$

$cot(theta) = 1/tan(theta) = 1/4$

$csc(theta) = +-sqrt(1 + cot^2(theta))$

$csc(theta) = +-sqrt(1 + (1/4)^2)$

$csc(theta) = +-sqrt(1 + 1/16)$

$csc(theta) = +-sqrt(17)/4$

It is impossible to tell whether to use the plus or minus case, without knowing whether the angle is in the first or the third quadrant.

How do you use tantheta=4tantheta=4 to find cscthetacsctheta?