find sino such that 3 coso L4 sino=4.
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what is l 4... and o..........
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◆ 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.
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.
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