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

Question

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

1 Answer

Impact of this question

3768 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-14T21:46:08

Use the identities $cot (θ) = \frac{1}{tan (θ)}$ $cot(theta)=1/tan(theta)$ and $csc (θ) = \pm \sqrt{1 + {cot}^{2} (θ)}$ $csc(theta) = +-sqrt(1 + cot^2(theta))$

Explanation:

$cot (θ) = \frac{1}{tan (θ)} = \frac{1}{4}$ $cot(theta) = 1/tan(theta) = 1/4$

$csc (θ) = \pm \sqrt{1 + {cot}^{2} (θ)}$ $csc(theta) = +-sqrt(1 + cot^2(theta))$

$csc (θ) = \pm \sqrt{1 + {(\frac{1}{4})}^{2}}$ $csc(theta) = +-sqrt(1 + (1/4)^2)$

$csc (θ) = \pm \sqrt{1 + \frac{1}{16}}$ $csc(theta) = +-sqrt(1 + 1/16)$

$csc (θ) = \pm \frac{\sqrt{17}}{4}$ $csc(theta) = +-sqrt(17)/4$

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.

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you use tanθ=4tantheta=4 to find cscθcsctheta?

1 Answer

Explanation:

Related questions

Impact of this question

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