Math, asked by abhishekyadav73031, 8 months ago

Find sinteta such that 3costeta + 4sinteta = 4​

Answers

Answered by naveenjoshi01974
3

Answer:

3/4sinteta

and 3/4*4

= 3 costeta

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Answered by trixy123
0

Answer:

sin θ = {1, 0.28}

Step-by-step explanation:

3\cos\theta+4\sin\theta=4\\\implies (3\cos\theta+4\sin\theta)^2=4^2\\\implies 9\cos^2\theta+16\sin^2\theta+24\sin\theta\cos\theta=16\\\implies 16\cos^2\theta+16\sin^2\theta-7\cos^2\theta+24\sin\theta\cos\theta=16\\\implies 16(\cos^2\theta+\sin^2\theta)-7\cos^2\theta+24\sin\theta\cos\theta=16\\\implies 16(1)-7\cos^2\theta+24\sin\theta\cos\theta=16\\\implies 24\sin\theta\cos\theta-7\cos^2\theta=16-16\\\implies \cos\theta(24\sin\theta-7\cos\theta)=0

Now, there are two possible answers:

\cos\theta=0\\\implies \theta=\cos^{-1}(0)\\\implies \theta=90

or

24\sin\theta-7\cos\theta=0\\\implies 24\sin\theta=7\cos\theta\\\implies \frac{\sin\theta}{\cos\theta}=\frac{7}{24}\\\\\implies \tan\theta=\frac{7}{24}\\\\\implies \theta=\tan^{-1}(\frac{7}{24})\\\implies \theta\approx 16.26

So,

if θ=90°,

\sin\theta=1

if θ=16.26,

\sin\theta\approx 0.28

{Use a calculator for the second case]

Hope it helps!

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