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suter [353]
2 years ago
15

Find all solutions to the equation in the interval [0, 2pi). COS X = sin 2x​

Mathematics
1 answer:
Lera25 [3.4K]2 years ago
6 0

Answer:

Step-by-step explanation:

cos x=sin 2x

sin 2x-cos x=0

2 sin x cos x-cos x=0

cos x(2 sin x-1)=0

either cos x=0

x=\frac{\pi }{2},\frac{3\pi }{2}

or

2 sin x-1=0

sin x=\frac{1}{2} =sin (\frac{\pi }{6}),sin(\pi -\frac{\pi }{6} )\\x=\frac{\pi }{6} ,\frac{5 \pi }{6}

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3 years ago
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Elan Coil [88]

 

Since pi is equivalent to 3.14 and means 180°, therefore 1.75 which is about half of pi should be at almost 90°. The cos of a 90° angle which is located on the y axis should be zero, therefore cos 1.75 must be near zero. However in this case it is near one, clearly his calculator is in degree mode that is why he got an erroneous answer.

What Sam can do to get the correct answer would be to convert his calculator into radian mode or convert the given 1.75 rad into degrees:

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<span>cos 100.2676 = -0.1782   which is now correct since it is nearer to zero</span>

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3 years ago
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2 years ago
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Step-by-step explanation:

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