Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

cos⁴ 135° is gelijk aan (Zonder rekentoestel uiteraard !)	A. $-\frac{1}{4}$
	B. $-\frac{1}{8}$
	C. $-\frac{1}{16}$
	D. $\frac{1}{4}$
	E. $\frac{1}{8}$
	F. $\frac{1}{16}$

[ 4-3323 - op net sinds 7.2.04-(E)-4.5.2025 ]

Translation in E N G L I S H

cos⁴ 135° = (Without any Calculator !)	A. $-\frac{1}{4}$
	B. $-\frac{1}{8}$
	C. $-\frac{1}{16}$
	D. $\frac{1}{4}$
	E. $\frac{1}{8}$
	F. $\frac{1}{16}$

Oplossing - Solution

$\\\cos^4\,{135^{\circ}}=(\cos\:135^{\circ})^4=(-\cos\:45^{\circ})^4=(\cos\:45^{\circ})^4\\=\left(\frac{\sqrt{2}}2{}\right)^4=\frac{\sqrt{2}\cdot\sqrt{2}\cdot\sqrt{2}\cdot\sqrt{2}}{2^{4}}=\frac{2\cdot 2}{16}=\cdots$

cos⁴ 135° is gelijk aan (Zonder rekentoestel uiteraard !)	A. \(-\frac{1}{4}\)
	B. \(-\frac{1}{8}\)
	C. \(-\frac{1}{16}\)
	D. \(\frac{1}{4}\)
	E. \(\frac{1}{8}\)
	F. \(\frac{1}{16}\)

cos⁴ 135° = (Without any Calculator !)	A. \(-\frac{1}{4}\)
	B. \(-\frac{1}{8}\)
	C. \(-\frac{1}{16}\)
	D. \(\frac{1}{4}\)
	E. \(\frac{1}{8}\)
	F. \(\frac{1}{16}\)