Question

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

Answer 1

Explanation:

First, use the Pythagorean theorem to find cos x.

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

`((7)/(9) ) {}^(2) + \cos {}^(2) (x) = 1`

`\cos {}^(2) (x) = 1 - (49)/(81)`

`\cos {}^(2) (x) = (32)/(81)`

`\cos(x) = (4 √(2) )/(9)`

Now, use the quotient identity

`\tan(x) = ( \sin(x) )/( \cos(x) )`

`\tan(x) = ( (7)/(9) )/( (4 √(2) )/(9) )`

`\tan(x) = (7)/(4 √(2) )`

`\tan(x) = (7 √(2) )/(8)`

The answer is A