sin θ = [tex]$\frac{-\sqrt{33} }{7}[/tex]
tan θ = [tex]$\frac{-\sqrt{33}}{4}[/tex]
Step-by-step explanation:
It is given that, cos θ = [tex]$\frac{4}{7}[/tex] then csc θ < 0, which implies that the θ is in the quadrant IV. Since cos θ is [tex]$\frac{adj}{hyp}[/tex] , 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 = [tex]\sqrt{33}[/tex]
Using the value of x, we can write the sine and tan ratio as,
sin θ = [tex]$\frac{opp}{hyp}[/tex] = [tex]$\frac{-\sqrt{33} }{7}[/tex]
tan θ =[tex]$\frac{opp}{adj}[/tex] = [tex]$\frac{-\sqrt{33}}{4}[/tex]
Thus we have obtained the values of sin θ and tan θ
