Question

Find all degree solutions for cos3x=0

Answer 1

`cos(3x)=0 \\cos(3x)=4cos^3(x)-3cos(x)\\-------------------- \\\\4cos^3(x)-3cos(x)=0 \\\\Factor\:out\:common\:term\: \\\\cos(x)(4cos^2(x)-3)=0 \\\\cos(x)=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4cos^2(x)-3=0`

`(90^(\circ ), 270^(\circ )) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4cos^2(x)=3 \\\\ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ cos^2(x) = (3)/(4) \\\\ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ √(cos^2(x))= \sqrt{(3)/(4) } \\\\ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ cos(x)= \pm ( √(3) )/(2)`

`\\\\ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (30^(\circ ),330^(\circ ),210^(\circ ),150^(\circ )) \\\\ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \theta _I=30\\ \\\\ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \theta_(II)=180-30 \\\\ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \theta_(II)= 150\\ \\\\ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \theta_(III)=30+180`

`\\\\ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \theta_(III)=210 \\ \\\\ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \theta_(IV)=360-30 \\\\ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \theta_(IV)=330`

The answer is {30, 90, 150, 210, 270, 330}