Question

What is the value of tan?

Answer 1

Answer: B. $\frac{4}{3}$ .

Step-by-step explanation:

• In a right triangle, the ratios of its sides are called trigonometric ratios.
• The three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

We have given , $\sin\theta=\dfrac{4}{5}\text{ and }\dfrac{\pi}{2}$.

Then, $\cos\theta =\sqrt{1-\sin^2\theta}\ [\because\ \sin^2A+\cos^2A=1]$

Put value of $\sin\theta$, we get

$\Rightarrow\ \cos\theta=\sqrt{1-(\frac{4}{5})^2}$

$\Rightarrow=\sqrt{1-\frac{16}{25}}=\sqrt{\frac{25-16}{25}}=\sqrt{\frac{9}{25}}=\frac{3}{5}$

Now , as we know , $\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac{4}{5}}{\frac{3}{5}}=\frac{4}{3}$

Hence, the correct option is B. $\frac{4}{3}$ .