Question

find sin theta such that 3 cos theta + 4 sin theta = 4​

Answer 1

Answer:

sinθ = 1 or sinθ = 7/25

Step-by-step explanation:

We'll substitute sinθ = x for easy calculations. Then cosθ = √(1-sin²θ) = √(1-x²).

Now given equation,

3cosθ + 4sinθ = 4  

3cosθ = 4 - 4sinθ

3 √(1-x²) = 4(1-x)

Squaring both sides,

9 (1-x²) = 16 (1-2x+x²)

9 - 9x² = 16 - 32x + 16x²

25x² - 32x + 7 = 0

Solving this quadratic eqn,

x = 1 or x = 7/25

sinθ = 1 or sinθ = 7/25

Hence, value of sinθ can be either 1 or 7/25.