Question

find tan (0) from sin 0= 7/9

Answer 1

Step-by-step explanation:

First, use the Pythagorean theorem to find cos x.

$\sin {}^{2} (x) + \cos {}^{2} (x) = 1$

$(\frac{7}{9} ) {}^{2} + \cos {}^{2} (x) = 1$

$\cos {}^{2} (x) = 1 - \frac{49}{81}$

$\cos {}^{2} (x) = \frac{32}{81}$

$\cos(x) = \frac{4 \sqrt{2} }{9}$

Now, use the quotient identity

$\tan(x) = \frac{ \sin(x) }{ \cos(x) }$

$\tan(x) = \frac{ \frac{7}{9} }{ \frac{4 \sqrt{2} }{9} }$

$\tan(x) = \frac{7}{4 \sqrt{2} }$

$\tan(x) = \frac{7 \sqrt{2} }{8}$

The answer is A