Question

if sin theta is equal to minus 1 by 3 and theta does not lie in third quadrant then find the values of cos theta cot theta​

Answer 1

Answer:

$\bf{cos\theta=\frac{2\sqrt2}{3}}$

$\bf{cot\theta=\frac{-1}{2\sqrt2}}}$

Step-by-step explanation:

Given:

$sin\theta=\frac{-1}{3}$

since $sin\theta$ is negative and $\theta$ does not lie in 3rd quadrant, $\theta$ lies in 4th quadrant

$cos^2\theta=1-sin^2\theta$

$\implies\:cos^2\theta=1-\frac{1}{9}$

$\implies\:cos^2\theta=\frac{9-1}{9}$

$\implies\:cos^2\theta=\frac{8}{9}$

$\implies\:cos\theta=\pm\frac{2\sqrt2}{3}$

$\text{But}\:\theta\:\text{lies in fourth quadrant}$

$\bf{\therefore\:cos\theta=\frac{2\sqrt2}{3}}$

Now,

$cot\theta=\frac{sin\theta}{cos\theta}$

$cot\theta=\frac{\frac{-1}{3}}{\frac{2\sqrt2}{3}}$

$\bf{cot\theta=\frac{-1}{2\sqrt2}}}$

Answer 2

Answer:

here is youranswer

Step-by-step explanation:

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