Question

Find all solutions of this equation in the interval [0,2pi]:

Answer 1

In radians,

x = (π/4)

OR

x = (7π/4)

In degrees,

x = 45°

OR

x = 315°

Step-by-step explanation

To solve for x in the given interval, we need to first isolate Cos x

2 cos (x) - √2 = 0

2 cos (x) = √2

Divide both sides by 2

Cos x = (√2)/2

So, we will now find the values of x in the interval [0, 2pi], that is, [0°, 360°]

We know that Cosine is positive only in the first and fourth quadrant.

So,

Cos x = (√2)/2

x = Cos⁻¹ (√2)/2

x = 45°

OR

x = 315°

In radians,

x = (π/4)

OR

x = (7π/4)

Hope this Helps!!!