Question

If $cos \theta=\frac{7}{25}$, then find the values of $cosec \theta \hspace{3}and \hspace{3} cot \theta$

Answer 1

Answer:

Step-by-step explanation:

Hope it works!!!!

Answer 2

Solution:

We know that

$cos \theta=\frac{Base}{Hypotenuse}\\\\cos \theta=\frac{7}{25} =k$

So Base = 7 k

Hypotenuse= 25 k

So,in a right angle triangle if Base and Hypotenuse is given so by Pythagoras theorem we can find perpendicular

${(perpendicular)}^{2} = {(hypotenuse)}^{2} - ( {base)}^{2} \\ \\ = ( {25k)}^{2} - ( {7k)}^{2} \\ \\ = 625 {k}^{2} - 49 {k}^{2} \\ \\ = 576 {k}^{2} \\ \\ perpendicular = \sqrt{576 {k}^{2} } = 24k$

Now to find

1)
$cosec \: \theta = \frac{hypotenuse}{perpendicular} \\ \\ cosec \: \theta = \frac{25k}{24k} \\ \\ cosec \: \theta = \frac{25}{24}$

2)
$cot \: \theta = \frac{base}{perpendicular} \\ \\ cot \: \theta = \frac{7k}{24k} \\ \\ cot \: \theta = \frac{7}{24}$

Hope it helps you.