Question

Write cos11π18 in terms of the cosine of a positive acute angle.

Answer 1

You have to use the fact that $\cos(\pi-x)=-\cos x$ for any value of $x$. So

$\cos\dfrac{11\pi}{18}=-\cos\left(\pi-\dfrac{11\pi}{18}\right)=-\cos\dfrac{7\pi}{18}$

where $\dfrac{7\pi}{18}$ is the positive acute angle you're looking for.

Answer 2

An Angle is said to be Acute , if it lies between 0° to 90°.

In terms of Radian

$\rightarrow 0\leq \text{Angle} < \frac{\pi}{2}\\\\ \rightarrow \cos \frac{11\pi }{18}\\\\=\cos(\pi -\frac{7\pi}{18})\\\\=-\cos( \frac{7\pi}{18})$

⇒Cos(π-A)= -Cos A, becuse cosine of An Angle is Negative in Second Quadrant.