Find all solutions to the equation 8cos(x+4)=1 in the interval 0≤x≤2π. If there is more than one answer, enter your answers as a comma separated list.

Question

Ive been struggling with this material and this type of question in particular, any help is appreciated!

Answer 1

I always find it easiest to make a substitution for the argument of the trig function so I will make a = x+4

8 cos(a) = 1.

cos(a)= 1/8 To find the angle take inverse cosine of both sides which gives an answer of 82.8 degrees and

360 - 82.81= 277.2 degrees

since a= x+4 our answers are 82.8 - 4 = 78.8 and

272.2 - 4 = 273.18

Answer 2