Page 3 - 11-Math-14 Solutions of Trignometric Equation

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version: 1.1
Example 2: Solve the equation: 1 + cos x = 0

Solution: 1 + cos x = 0

⇒ cos x = -1

Since cos x is -ve, there is only one solution x = p in [0, 2p]

Since 2p is the period of cos x n∈Z
∴ General value of x is p + 2np,

Hence solution set = {p + 2np}, n ∈ Z

Example 3: Solve the equation: 4 cos2x - 3 = 0

Solution: 4 cos2 x - 3 = 0

⇒ cos2 x =3 ⇒ cos x =± 3
4 2

i. If cos x = 3
2

Since cos x is +ve in I and IV Quadrants with the reference angle

x= where x ∈[0, 2 ]
6

=∴ x and x== 2 - 11
6 66

As 2p is the period of cos x.

∴ General value of x are 6 + 2n and 11 + 2n , n∈Z
6

ii. if cos x = - 3
2

Since cos x is -ve in II and III Quadrants with reference angle x = 6

∴ x = - =5 and x = x + = 7 where x ∈[0, 2 ]
66 66

As 2p is the period of cos x.

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