Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\large \dpi{110}\frac{\sin 2000^\circ}{\sin 20^\circ}+\frac{\cos 2000^\circ}{\cos 20^\circ}$ is gelijk aan	A. − 1
	B. − 2
	C. 0
	D. een irrationaal getal
	E. geen van de vorige

[ 4-2241 - op net sinds 20.8.12-(E)-3.11.2023 ]

Translation in E N G L I S H

$\frac{\sin 2000^\circ}{\sin 20^\circ}+\frac{\cos 2000^\circ}{\cos 20^\circ}$ is equal to	A. − 1
	B. − 2
	C. 0
	D. an irrational number
	E. none of the above

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}5\!\times\!360^\circ=1800^\circ \qquad 2000^\circ\!-\!1800^\circ=200^\circ\\\frac{\sin 2000^\circ}{\sin 20\circ}\!+\!\frac{\cos 2000^\circ}{\cos 20^\circ}=\frac{\sin 200^\circ}{\sin 20^\circ}\!+\!\frac{\cos 200^\circ}{\cos 20^\circ}=\frac{-\sin 20^\circ}{\sin 20^\circ}\!+\!\frac{-\cos 20^\circ}{\cos 20^\circ}=-1-1=..$