## JayDelV one year ago If sin θ = 3 over 7 and tan θ < 0, what is the value of cos θ?

1. Nnesha

|dw:1439502598438:dw| at which quadrant sin is positive

2. JayDelV

First

3. Nnesha

remember that CAST rule for signs

4. Nnesha

yes first and ?

5. JayDelV

Oh and second

6. Nnesha

yes right sin positive in 1st and 2nd quadrant given is tan < 0 is is less than 0 so at which quadrant you should draw a right triangle ?

7. JayDelV

second?

8. Nnesha

yes right tan is negative in 2nd quadrant <0 |dw:1439502785727:dw| draw a right triangle $\rm sin \rm \theta = \frac{ opposite }{ hypotenuse }~~~~ \cos \theta = \frac{ adjacent }{ hypotenuse } ~~\tan \theta = \frac{ opposite }{ adjacent }$

9. Nnesha

sin = opposite over hyp so $\huge\rm \sin \theta = \frac{ 3 }{ 7 }=\frac{ opposite }{ hyp }$ opposite =3 hyp = 7 |dw:1439502881389:dw|

10. Nnesha

now apply the Pythagorean theorem to find 3rd side of right triangle

11. Nnesha

$\huge\rm a^2+b^2=c^2$ c=hypotenuse