Question

Given that sin θ ≈ −0.866, where π < θ < 3 , 2 π find cos θ.

Answer 1

Answer:

$\cos( \theta) = - 0.5$

Step-by-step explanation:

It was given that sin θ ≈ −0.866.

To find cosθ, we apply the Pythagorean property;

$\cos^{2} ( \theta) + \sin^{2} ( \theta) = 1$

$\implies \cos^{2} ( \theta) = 1 - \sin^{2} ( \theta)$

We substitute the given value to get:

$\cos^{2} ( \theta) = 1 -(0.866)^{2}$

$\cos^{2} ( \theta) = 0.250$

Take square root of both sides:

$\cos( \theta) = \pm \sqrt{0.250}$

$\cos( \theta) = \pm0.5$

But we were given that:

$\pi \leqslant \theta \: \leqslant \frac{3 \pi}{2}$

which is the third quadrant and we know the cosine function is negative in this quadrant.

Hence

$\cos( \theta)= - 0.5$