Question

If cotθ = 4/3, the find the value of 5sinθ + 4cosθ – 3.

• A. 5/6
• B. 14/5
• C. 16/5
• D. 4/5

Answer 1

Answer:

C. 16/5

Solution:

Given:

cotθ = 4/3

Concept used:

Using Pythagorean Theorem:

P² + B² = H²

Calculation:

cotθ = B/P = 4/3

Let B and P be 4x and 3x respectively.

(3x)² + (4x)² = H²

⇒ 9x² + 16x² = H²

⇒ 25x² = H²

⇒ H = 5x

5sinθ + 4cosθ – 3

⇒ 5 × (P/H) + 4 × (B/H) – 3

⇒ 5 × (3x/5x) + 4 × (4x/5x) – 3

⇒ 3 + 16/5 – 3

⇒ 16/5

∴ The value is 16/5.