Question

MULTIPLE CHOICE, PLS HELP!!

Answer 1

We know that : Sin²θ + Cos²θ = 1

Given : Sinθ $\bf{= \frac{4}{7}}$

$\bf{\implies (\frac{4}{7})^2 + Cos^2(\theta) = 1}$

$\bf{\implies Cos^2(\theta) = 1 - \frac{16}{49}}$

$\bf{\implies Cos^2(\theta) =(\frac{49 - 16}{49})}$

$\bf{\implies Cos^2(\theta) =(\frac{33}{49})}$

$\bf{\implies Cos(\theta) = (\pm)(\frac{\sqrt{33}}{7})}$

Given : θ lies in Quadrant II

We know that : Cosθ is Negative in Quadrant II

$\bf{\implies Cos(\theta) = (-)(\frac{\sqrt{33}}{7})}$

Option 3 is the Answer