Finf the solution that satisfy √3secx=-2if 0° ≤x≤360°?

To solve the equation √3sec(x) = -2, we first need to isolate sec(x) by dividing both sides by √3:

sec(x) = -2/√3

Next, we know that sec(x) is the reciprocal of cos(x), so we can rewrite the equation as:

cos(x) = -√3/2

Now, we need to find the angle x in the interval 0° ≤ x ≤ 360° where the cosine function equals -√3/2. This occurs in the second and third quadrants, where the cosine function is negative.

In the second quadrant, the reference angle for cos(x) = -√3/2 is 30° (cosine of 30° is √3/2). Therefore, x = 180° + 30° = 210°.

In the third quadrant, the reference angle for cos(x) = -√3/2 is also 30°. Therefore, x = 360° - 30° = 330°.

Therefore, the solutions that satisfy the equation √3sec(x) = -2 in the interval 0° ≤ x ≤ 360° are x = 210° and x = 330°.