Question

if 2sin theta+1=0 and 90°270° calculate a) 4cos²theta. b) 81tan²theta​

Answer 1

Answer:

A) $4\cos^2\theta=3$

B) $81\tan^2\theta=27$

Step-by-step explanation:

$\displaystyle 2\sin\theta+1=0;\:90^\circ \leq\theta\leq 270^\circ\\\\2\sin\theta=1\\\\\sin\theta=\frac{1}{2}\\ \\\theta=\frac{5\pi}{6}$

$\displaystyle 4\cos^2\theta=4\cos^2\biggr(\frac{5\pi}{6}\biggr)=4\biggr(-\frac{\sqrt{3}}{2}\biggr)^2=4\biggr(\frac{3}{4}\biggr)=3$

$\displaystyle 81\tan^2\theta=81\tan^2\biggr(\frac{5\pi}{6}\biggr)=81\biggr(-\frac{\sqrt{3}}{3}\biggr)^2=81\biggr(\frac{3}{9}\biggr)=81\biggr(\frac{1}{3}\biggr)=\frac{81}{3}=27$