Question

Question18 (5pt)!!!!!!!!!!

Answer 1

sin θ = $\frac{-\sqrt{33} }{7}$

tan θ = $\frac{-\sqrt{33}}{4}$

Step-by-step explanation:

It is given that, cos θ = $\frac{4}{7}$  then csc θ < 0, which implies that the θ is in the quadrant IV. Since cos θ is $\frac{adj}{hyp}$ , 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 = $\sqrt{33}$

Using the value of x, we can write the sine and tan ratio as,

sin θ = $\frac{opp}{hyp}$ = $\frac{-\sqrt{33} }{7}$

tan θ =$\frac{opp}{adj}$ = $\frac{-\sqrt{33}}{4}$

Thus we have obtained the values of sin θ and tan θ