Precalc help asap please?

Question

Solve the following equations; exact solutions in radians. Find all solutions. 
A.) Sin x= -1/2 
B.) Sec x = -sqrt 2 
I forgot how to do this so please explain well

Answer 1

(A).

The equation is sin(x) = - 1/2.

sin(x) = - sin(π/6)

sin(x) = sin(- π/6)

General solution : If sin(θ) = sin(α) then θ = nπ + (-1)ⁿα, where n is an integer.

If α = - π/6, then general solution x = nπ - (-1)ⁿ(π/6), where n is an integer.

(B).

The equation is sec(x) = - √2.

sec(x) = - sec(π/4)

sec(x) = sec(- π/4)

General solution : If sec(θ) = sec(α) then θ = 2nπ ± α, where n is an integer.

If α = - π/4, then general solution x = 2nπ ∓ π/4, where n is an integer.