Question

Find the value of θ from the following:

cos (2θ – 50°) = sin 60°

Answer 1

Given: cos (2θ – 50°) = sin 60°

Step-wise calculation:

1. Convert sin ⇒ cos using (sin x = cos (90° – x)):

sin 60° = cos (90° – 60°)

= cos 30°

So, the equation becomes cos (2θ – 50°) = cos 30°.

2. If cos A = cos B, then A = 360°k ± B, where k ∈ Z.

Hence, 2θ – 50° = 360°k + 30° or 2θ – 50° = 360°k – 30°.

3. Solve each case:

Case (i): 2θ – 50° = 360°k + 30°

2θ = 360°k + 80°

θ = 180°k + 40°

Case (ii): 2θ – 50° = 360°k – 30°

2θ = 360°k + 20°

θ = 180°k + 10°

θ = 180°k + 40° or θ = 180°k + 10°, k ∈ Z

If θ is restricted to (0° ≤ θ ≤ 180°), then (θ = 40°) or (θ = 10°).