Question

if sin theta is equals to 7 upon 25 find the values of cos theta and tan theta

Answer 1

Here's the answer

Given =>

$\sf{sin \: \theta = \frac{7}{25}}$

We know that ,

$\sf{sin {}^{2} \theta + cos {}^{2} \theta = 1}$

$\sf{({ \frac{7}{25}}) {}^{2} + cos {}^{2} \theta = 1}$

$\sf{cos {}^{2} \theta = 1 - ( \frac{7}{25}) {}^{2}}$

$\sf{cos {}^{2} \theta = 1 - \frac{49}{625}}$

$\sf{cos {}^{2} \theta = \frac{625 - 49}{625}}$

$\sf{cos {}^{2} \theta = \frac{576}{625}}$

Taking square roots on both the sides,

$\sf{ \boxed {cos {}^{2} \theta = \frac{24}{25}}}$
_____________________________

Now,
$\sf{tan \theta = \frac{sin \theta}{cos \theta}}$

$\therefore \sf{tan \theta = \frac{ \frac{7}{25} }{ \frac{24}{25}} }$

$\sf{ \therefore \: tan \theta = \frac{7}{25} \times \frac{25}{24}}$

$\sf{ \therefore \tan \theta = \frac{7}{{ \cancel 25}} \times \frac{ \cancel25}{24}}$

$\sf{ \boxed {\therefore \: tan \theta = \frac{7}{24}}}$

Final answer =>

$\sf{cos \theta = \frac{24}{25}}$

${\sf {\tan \theta = \frac{7}{24}}}$