Question

Find Sin theta such that 3cos theta+ 4sin theta =4

Answer 1

Step-by-step explanation:

Explanation

substitute sin theta = X

then cos theta =√(1-sin2 theta) =√(1-x2)

Now given equation,

3cos theta + 4 sin theta =4

3cos theta=4-4sin theta

3√(1-X2)=4(1-X)

squaring on both sides,

9(1-x2) =16(1-2x+x2)

9-9x2=16-32x+16x2

25x2-32x+7=0

solve quadratic equation,

x=1 or x=7/25

Hence, value of sin theta can be either 1 or

7/25

Answer 2

Answer:

{1, 7/25}

Step-by-step explanation:

$3\cos\theta+4\sin\theta=4\\\implies 3\cos\theta=4(1-\sin\theta)\\\implies 9\cos^2\theta=16(1-\sin\theta)^2\\\implies 9(1-\sin^2\theta)=16(1+\sin^2\theta-2\sin\theta)\\\implies 16+16\sin^2\theta-32\sin\theta-9+9\sin^2\theta=0\\\implies 25\sin^2\theta-32\sin\theta+7=0$

Using Quadratic Formula,

$\sin\theta=\frac{-(-32)\pm\sqrt{(-32)^2-4(25)(7)}}{2(25)}\\\\=\frac{32\pm\sqrt{1024-700}}{50}\\\\=\frac{32\pm\sqrt{324}}{50}\\\\=\frac{32\pm18}{50}\\\\=\{1,\frac{14}{50}\}\\\\=\{1,\frac{7}{25}\}$

Hope it helps!

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