If $cot θ = - 2$ $cot theta = - 2$ and $cos θ < 0$ $cos theta < 0$ , how do you find $sin θ$ $sintheta$ ?

Question

If $cot θ = - 2$ $cot theta = - 2$ and $cos θ < 0$ $cos theta < 0$ , how do you find $sin θ$ $sintheta$ ?

1 Answer

Impact of this question

29909 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-30T21:28:08

Start with the identity:

$1 + {cot}^{2} (θ) = {csc}^{2} (θ)$ $1+ cot^2(theta)=csc^2(theta)$

Explanation:

Substitute ${cot}^{2} (θ) = {(- 2)}^{2}$ $cot^2(theta) = (-2)^2$ :

$1 + {(- 2)}^{2} = {csc}^{2} (θ)$ $1+ (-2)^2=csc^2(theta)$

$5 = {csc}^{2} (θ)$ $5 = csc^2(theta)$

Substitute ${csc}^{2} (θ) = \frac{1}{{sin}^{2} (θ)}$ $csc^2(theta) = 1/sin^2(theta)$

$5 = \frac{1}{{sin}^{2} (θ)}$ $5 = 1/sin^2(theta)$

${sin}^{2} (θ) = \frac{1}{5}$ $sin^2(theta) = 1/5$

$sin (θ) = \pm \frac{\sqrt{5}}{5}$ $sin(theta) = +-sqrt5/5$

Because we are told that $cos (θ) < 0$ $cos(theta) < 0$ and $cot (θ) = - 2$ $cot(theta) = -2$ , we know that the sine function must be positive in this quadrant:

$sin (θ) = \frac{\sqrt{5}}{5}$ $sin(theta) = sqrt5/5$

Science

Math

Humanities

... and beyond

If $cot θ = - 2$ $cot theta = - 2$ and $cos θ < 0$ $cos theta < 0$ , how do you find $sin θ$ $sintheta$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

If cot theta = - 2cotθ=−2cot theta = - 2 and cos theta < 0cosθ<0cos theta < 0, how do you find sinthetasinθsintheta?

1 Answer

Explanation:

Related questions

Impact of this question

If $cot θ = - 2$ $cot theta = - 2$ and $cos θ < 0$ $cos theta < 0$ , how do you find $sin θ$ $sintheta$ ?