Question

find all degree solutions. cos 4 theta = 0

Answer 1

first let me ask you this, cosx=0 what can x be?

Answer 2

\(\bf \textit{what's}\quad cos^{-1}[cos(\theta)]\quad ?\)

Answer 3

1?

Answer 4

90

Answer 5

1?

Answer 6

h.mmm say what's the \(\bf cos(90^o)\quad ?\)

Answer 7

cos (90) = 0 right?

Answer 8

yes.... what's \(\bf cos^{-1}(0)\quad ?\)

Answer 9

90!

Answer 10

\(\bf cos(90^o)=0\qquad cos^{-1}(0)=90^o\qquad \textit{which means}\\ \quad \\
cos^{-1}[cos(90^o)] = 90^o\implies cos^{-1}[cos(\theta)]=\theta\qquad thus\\ \quad \\
cos(4\theta)=0\qquad \textit{taking }cos^{-1}\textit{ to both sides}\\ \quad \\
cos^{-1}[cos(4\theta)]=cos^{-1}[0]\implies 4\theta=cos^{-1}[0]\implies \theta=\cfrac{cos^{-1}[0]}{4}
\)