Explanation:
If cosθ = 4/7, we can represent it with the following triangle
To find the sinθ, we need to calculate the missing side x. Using the Pythagorean theorem, we get that the value of x is
[tex]\begin{gathered} x=\sqrt{7^2-4^2} \\ x=\sqrt{49-16} \\ x=\sqrt{33} \end{gathered}[/tex]
Then, sinθ and cscθ have the same sign, so sinθ will be negative and is equal to
[tex]\begin{gathered} \sin\theta=\frac{Opposite}{Hypotenuse} \\ \\ \sin\theta=\frac{x}{7} \\ \\ \sin\theta=-\frac{\sqrt{33}}{7} \end{gathered}[/tex]
Finally, tanθ is equal to
[tex]\begin{gathered} \tan\theta=\frac{Opposite}{Adjacent} \\ \\ \tan\theta=\frac{-\sqrt{33}}{4} \end{gathered}[/tex]
Answer:
Therefore, the answer is
[tex]\sin\theta=\frac{-\sqrt{33}}{7},\tan\theta=\frac{-\sqrt{33}}{4}[/tex]
