1) 2sin x = -1, 2) sin x/3 = - ✓3/2, 3) 2cos x + 1 = 0, 5) cos(x - π/4) = 0

Question

1) 2sin x = -1, 2) sin x/3 = - ✓3/2, 3) 2cos x + 1 = 0, 5) cos(x - π/4) = 0

Answer 1

Sinx = -1/2; x = 7π/6 +2πn; n∈Z.   2)  x/3 = -4π/3 +2πn; n∈Z;  x =-4π+2πn/3; n∈Z; 3) 2cosx = -1/2; cosx =1/4;  x = argcos1/4 +2πn; n∈Z;

5) x - π/4 = π/2+kπ;   x = π/2+π/4+kπ= 3π/4+kπ;