Question

If cot $\theta =2$, find the values of all T-ratios of $\theta$.

Answer 1

We know that, $1+co{t}^2\theta =cose{c}^2\theta$

$1+4=cose{c}^2\theta$

$cose{c}^2\theta =\sqrt{5}$

$cosect\theta =\sqrt{5}$

therefore $sin\theta =\frac{1}{\sqrt{5}}$

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

$2=\frac{cos\theta }{\left(\frac{1}{\sqrt{5}}\right)}$

$cos\theta =\frac{2}{\sqrt{5}}$

therefore

$sec\theta =\frac{\sqrt{5}}{2}$

$tan\theta =\frac{1}{cot\theta }=\frac{1}{2}$

$sin\theta =\frac{1}{\sqrt{5}}$
$cos\theta =\frac{2}{\sqrt{5}}$
$tan\theta =\frac{1}{2}$
$cosec\theta =\sqrt{5}$
$sec\theta =\frac{\sqrt{5}}{2}$