6. (a) Given that sin θ = 5 cos θ, find the value of tan θ - Edexcel - A-Level Maths Pure - Question 8 - 2006 - Paper 2

We already established that tan θ = 5. Now we find the angle θ:

Using the inverse tangent function:

$$θ = an^{-1}(5)$$

Calculating this gives:

$$θ ≈ 78.7°$$

Since the tangent function is positive in both the first and third quadrants, we find the second solution by adding 180°:

$$θ = 78.7° + 180° ≈ 258.7°$$

Thus, the values of θ are approximately:

$$θ ≈ 78.7° ext{ and } 258.7°$$

Both answers are rounded to 1 decimal place.