Question

State as subsets of R the domains of the cosine and secant functions. Find all −π < x π such that cos2x = 0.

Answer 1

Answer:

x  = -3π/4  , -π/4  , π/4  , 3π/4  

Step-by-step explanation:

domains of the cosine =   R

domains of the Secants  = R  except   ±(2n+1) π/2

−π < x π

=> −2π < 2x 2π

Cos2x = 0

Cos 90° = Cos(π/2) = 0

Cos -90° = Cos(-π/2) = 0

Cos 270° = Cos(3π/2) = 0

Cos -270° = Cos(-3π/2) = 0

=> 2x   =  -3π/2  , -π/2  , π/2  , 3π/2  

=> x  = -3π/4  , -π/4  , π/4  , 3π/4