Question

Solve the following trigonometric equation:

Answer 1

45, 135, 195 and 345degrees

Explanation:

Solve the following trigonometric equation:

2sin^22x + sin2x - 1 = 0

Let P = sin2x

Substitute

2P^2 - P - 1 = 0

Factorize;

2P^2 - 2P+P - 1 = 0

2P(P-1)+1(P-1) = 0

(2P+1)(P-1) == 0

2P+1 = 0 and P -1 = 0

P = -1/2 and 1

Since P = sin2x

sin2x = 1

2x = arcsin1

2x = 90

x = 90/2

x = 45degrees

Since sin is positive in the second quadrant

x = 180 - 45

x = 135 degrees

sin2x = -1/2

2x = arcsin(-0.5)

2x = -30

x = -15

Since sin is negative in the third and 4th quadrant

x = 180 + 15 = 195

x = 360 - 15 = 345

Hence the value of x are 45, 135, 195 and 345degrees