Question

Express the number tan(arcsin(24/25)) in the form of a reduced fraction p/q (such as 2/3, 4/5, −1/4, etc.) with q>0 and give the integers p and q.

Answer 1

Answer on Question #57482 – Math – Trigonometry

Question

Express the number $\tan(\arcsin(24/25))$ in the form of a reduced fraction $p/q$ (such as $2/3, 4/5, -1/4$, etc.) with $q > 0$ and give the integers $p$ and $q$.

Solution

$$\begin{array}{l} \tan \left(\arcsin \frac{24}{25}\right) = \frac{\sin \left(\arcsin \frac{24}{25}\right)}{\cos \left(\arcsin \frac{24}{25}\right)} = \frac{\frac{24}{25}}{\sqrt{1 - \sin^2 \left(\arcsin \frac{24}{25}\right)}} = \\ = \frac{\frac{24}{25}}{\sqrt{1 - \left(\frac{24}{25}\right)^2}} = \frac{\frac{24}{25}}{\sqrt{1 - \frac{576}{625}}} = \frac{\frac{24}{25}}{\sqrt{\frac{49}{625}}} = \frac{24}{7} = \frac{p}{q} \end{array}$$

Answer: $24/7$, $p = 24$, $q = 7$.

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