If pi/2≤θ≤π and sin θ =4/5, find the exact value of cosθ and cotθ?

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If pi/2≤θ≤π and sin θ =4/5, find the exact value of cosθ and cotθ?

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Answer 1 · 2017-10-25T07:45:01

$cos (θ) = \frac{3}{5}$ $cos(theta)= 3/5$

$cot (θ) = \frac{3}{4}$ $cot(theta)=3/4$

Explanation:

First let's state what we know.

1). ${sin}^{2} (θ) + {cos}^{2} (θ) = 1$ $sin^2(theta)+cos^2(theta)=1$

2). $\frac{sin (θ)}{cos (θ)} = tan (θ)$ $sin(theta)/cos(theta)=tan(theta)$

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

So we have:

${(\frac{4}{5})}^{2} + {cos}^{2} (θ) = 1 \Rightarrow {cos}^{2} (θ) = 1 - \frac{16}{25} = \frac{9}{25}$ $(4/5)^2+cos^2(theta)=1=>cos^2(theta)=1-16/25=9/25$

$\to {cos}^{2} (θ) = \frac{9}{25}$ $->cos^2(theta)=9/25$

Taking roots:

$cos (θ) = \frac{\sqrt{9}}{\sqrt{25}} = \frac{3}{5}$ $cos(theta)= (sqrt(9))/(sqrt(25))=color(blue)(3/5)$

$cot (θ) = \frac{1}{\frac{sin (θ)}{cos (θ)}} = \frac{1}{\frac{\frac{4}{5}}{\frac{3}{5}}} = \frac{1}{\frac{4}{3}} = \frac{3}{4}$ $cot(theta)= (1)/((sin(theta))/(cos(theta)))=1/((4/5)/(3/5))=1/(4/3)=color(blue)(3/4)$

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If pi/2≤θ≤π and sin θ =4/5, find the exact value of cosθ and cotθ?

I tried doing this problem but got stuck midway through. I need some help finishing this problem

1 Answer

Explanation:

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