Question

If \[\sin\theta = \frac{7}{25}\], find the values of cosθ and tan​θ.

Answer 1

We have, 
\[\sin^2 \theta + \cos^2 \theta = 1\]
\[ \Rightarrow \left( \frac{7}{25} \right)^2 + \cos^2 \theta = 1\]
\[ \Rightarrow \cos^2 \theta = 1 - \frac{49}{625} = \frac{625 - 49}{625} = \frac{576}{625}\]

\[ \Rightarrow \cos\theta = \sqrt{\frac{576}{625}} = \frac{24}{25}\]
Now,
\[\tan\theta = \frac{\sin\theta}{\cos\theta}\]
\[ \Rightarrow \tan\theta = \frac{\frac{7}{25}}{\frac{24}{25}}\]
\[ \Rightarrow \tan\theta = \frac{7}{24}\]
Thus, the values of cosθ and tanθ are \[\frac{24}{25}\] and \[\frac{7}{24}\], respectively.