Question

Please help how do you solve this?

Answer 1

x=π/9+2πn/3, 5π/9+2πn/3

Answer 2

x=π/9+2πn/3, 5π/9+2πn/3, for any integer n

Explanation:

Given:

cos3Ф=1/2

taking inverse cosine on both sides

cos^-1(cos3Ф)= cos^-1 (1/2)

3Ф=π/3

Ф=π/9

for second solution, subtracting π/3 from 2π

3Ф=2π-π/3

= 5π/3

Ф=5π/9

here period of the function is 2π/3

Hence the value of cos3Ф will repeat after every 2π/3

x=π/9+2πn/3, 5π/9+2πn/3, for any integer n !