Question

BRAINLIEST!

Answer 1

Answer:

cosθ = - $\frac{\sqrt{33}}{7}$.

Step-by-step explanation:

Given  : sinθ=$\frac{4}{7}$.

To find : What is the exact value of cosθ in simplified  form .

Solution : We have given sinθ=$\frac{4}{7}$.

By the trigonometric identity : $(sin)^{2} +(cos)^{2} = 1$.

Plug the value of sinθ=$\frac{4}{7}$.

$(\frac{4}{7}) ^{2} + cos^{2} = 1$.

$(\frac{16}{49}) + cos^{2} = 1$.

Subtracting $\frac{16}{49}$  from both sides

$cos^{2} = 1 - \frac{16}{49}$.

$cos^{2} = \frac{49 -16}{49}$.

$cos^{2} = \frac{33}{49}$.

Taking square root both sides

$cos ( theta) = \sqrt{\frac{33}{49} }$.

cosθ = ± $\frac{\sqrt{33}}{7}$.

θ lies in Quadrant II so,  cosθ = - $\frac{\sqrt{33}}{7}$.

Therefore, cosθ = - $\frac{\sqrt{33}}{7}$.

Answer 2

sin theta = 4/7

theta = arcsin (4/7)

cos (arcsin (4/7)

if theta is in the second quadrant cos theta is negative (calculators only give the postive answer)

cos (arcsin (4/7)= - sqrt(33)/7

Choice B