Solve the following Trig equations finding all solutions and

Solve the following Trig equations finding all solutions and the specific solutions in [0, 2 pi]. a) 2 cos x + 1 = 0 b) Squareroot 3 cot x = 1 c) sec^2 x - 2 = 0 d) 4 sin^2 theta = 1

Solution

Solution:

2Cos(x) +1 = 0

2Cos(x) = -1

Cos(x) = -1/2

x = 2/3 +2n and 4/3 + 2n

x = 2/3 and 4/3

(b) 3 Cot(x) = 1

Cot(x) = 1/3

x = /3 and 4/3

(c)

sec²(x) - 2 = 0

sec(x) = +/- 2

Sec(x) = 2

x = /4 and 7/4

sec(x) = -2

x = 3/4 and x = 5/4

Answer

(d) 4sin²() = 1

Sin() = +/-1/2

Sin() = 1/2

=/6 and    =5/6

and

Sin() = -1/2

= 7/6 and =11/6

Answer :