Question

all degree solutions for: cos 4x=-1

Answer 1

try u substitution. set u=4x, and solve like a normal equation. then substitute 4x back in

Answer 2

cos4x= 8cos^4(x) - 8cos^2(x) + 1

now 8cos^4(x) - 8cos^2(x) + 1=-1

cos^2x= a

8a^2-8a +1 =-1

8a^2 -8a +2 =0

a=1/2

since its a Sqr root answers will be +sqr 1/2 and -sqr 1/2

angle will be = 60 deg

now from unit circle

Cos is positive in 1st and last quadrants hence answers will be = 60 deg and 300 deg

cos is negative in 2nd and 3rd quadrants hence answers will be = 120 deg and 240 deg

Answer 3

the general formula for the solution when the coefficient a is other than 1 or -1 is \[ax=x_i+n(360)\] for integers n=0,1,2,..., a-1

Answer 4

is it cos^4(x) or cos(4x)??

Answer 5

where \[x_i\] is a solution you get via a calculator (or inspection)
for the problem, \[x_i=180\]

Answer 6

ugh. \[\cos x=\frac{ \sqrt{2} }{ 2 }\] so \[x=45^o\] and not 60 degrees.

Answer 7

well done sirm! so lets correct the answers
45 and 315

135 and 225