Three smallest positive solutions

Question

Solve for the smallest three positive solutions. Give your answers accurate to at least two decimal places, as a list separated by commas

Answer 1

cos(2x) = 3/4

Cosine is positive in quadrants 1 and 4.

Cos^-1(3/4) = 0.72 radians

2x = 0.72 + 2kπ or (2π - 0.72) + 2kπ = 0.72 + 2kπ or 5.56 + 2kπ

So, x = 0.36 + kπ or 2.78 + kπ where k = 0, ±1, ±2, ...

If k = 0, we get x = 0.36, or 2.78

If k = 1, we have x = 3.50 or 5.92, etc.

The 3 smallest positive solutions are 0.36, 2.78, 3.50 (answers are in radians)

Answer 2

4cos(2x)=3

cos(2x)=.75

cos41.4096...........=.75

x=20.7048.......°