Determine the exact value of 𝑥 the following expression given that 0 ≤ 𝑥 ≤ 90.

Question

2squareroot2𝑐𝑜𝑠𝑥 = 2

Answer 1

To determine the exact value of 𝑥 in the given expression, we need to solve the equation:

2√2cos𝑥 = 2

Divide both sides of the equation by 2:

√2cos𝑥 = 1

Divide both sides of the equation by √2:

cos𝑥 = 1/√2

To find the values of 𝑥 where cos𝑥 equals 1/√2, we can use the inverse cosine function. Remember that the inverse cosine function gives values in the range [0, π] or [0°, 180°].

cos⁻¹(1/√2) ≈ 45°

Therefore, 𝑥 can be 45 degrees.