For each of the equations below, write the general solution, in positive radians. Use mathematics to explain how you determined your answers.

Question

A) sin x + 1= 1.456

B) 9cos^2 x + 1 =8

Answer 1

A) sinx = 0.456; x = sin^-1(0.456) + 2πn = 0.4735 + 2πn, n ∈ Z

or x = π - sin^-1(0.456) + 2πn = 2.6681 + 2πn, n ∈ Z

B) 9cos²x + 1 = 8; cos2x + 1 = 14/9; cos2x = 5/9

2x = cos^-1(5/9) + 2πn or 2x = 2π - Cos^-1(5/9) + 2πn;

x = 0.4909 + πn;

or x = 2.6507 + πn

n ∈ Z