sin θ = ![$\frac{-\sqrt{33} }{7}](https://tex.z-dn.net/?f=%24%5Cfrac%7B-%5Csqrt%7B33%7D%20%7D%7B7%7D)
tan θ = ![$\frac{-\sqrt{33}}{4}](https://tex.z-dn.net/?f=%24%5Cfrac%7B-%5Csqrt%7B33%7D%7D%7B4%7D)
<u>Step-by-step explanation:</u>
It is given that, cos θ =
then csc θ < 0, which implies that the θ is in the quadrant IV. Since cos θ is
, we need to find the opposite side x.
Using the Pythogarus theorem, we can find the sin and the tan θ as,
7² = 4² + x²
x² = 7² - 4²
x² = 49 - 16
x² = 33
Taking sqrt on both sides, we will get,
x = ![\sqrt{33}](https://tex.z-dn.net/?f=%5Csqrt%7B33%7D)
Using the value of x, we can write the sine and tan ratio as,
sin θ =
= ![$\frac{-\sqrt{33} }{7}](https://tex.z-dn.net/?f=%24%5Cfrac%7B-%5Csqrt%7B33%7D%20%7D%7B7%7D)
tan θ =
= ![$\frac{-\sqrt{33}}{4}](https://tex.z-dn.net/?f=%24%5Cfrac%7B-%5Csqrt%7B33%7D%7D%7B4%7D)
Thus we have obtained the values of sin θ and tan θ