Solve the following trigonometric equations

Question

Solve the following trigonometric equations

 

(a) 2 cos θ +√3 = 0, 0 ≤ θ ≤ 2π

 

 

(b) tan x = √2sinx, 0 ≤ x ≤ 2π

 

(c) sec ² x−1 = 0, 0 ≤ x ≤ 2π

 

(d) 2sin² x−sin x−1 = 0, −2π ≤ x ≤ 2π

Answer 1

a) cos x=-√3/2

 so x=5*pi/6

 

b) sin x/cos x=√2sinx

 

eliminate sin x both sides

 

cos x=1/√2

 

x=pi/4

 

c) sec ² x=1 or -1

 

sec  x=1 or -1

 

cos x=1 or -1

 

x=0,pi,and 2*pi

 

d) substitute y=sin x

 

2y²-y-1=0

 

the solutions are {1,-0.5}

 

If sin x=1  x is pi/2

 

If sin x=-0.5 x=7*pi/12