Question

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

Answer 1

Hey Dear,

◆ Answer -

sinθ = 1 or sinθ = 7/25

● Explaination -

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.

Thanks dear..

Answer 2

Answer

sin theta = 1

Step-by-step explanation:

3 cos theta + 4sin theta = 4

3 cos theta = 4 - 4 sin theta

3(√1 - sin^2 theta) = 4 - (4 sin theta) ......(cos^2theta+sin^2theta=1)

squaring both side...

9√1 - sin^2 theta = 16 - 16 sin^2 theta

9 - 9 sin^2 theta = 16 - 16 sin^2 theta

- 9 sin^2 theta + 16 sin^2 theta = 16 - 9

7 sin^2 theta = 7

sin^2 theta = 7/7

sin theta =√7/7

sin theta = 1