Question

Sin32sin148 - cos32sin302 + ctg225

Answer 1

Ответ:

~ -0,911806 (~) этот значок обозначает приблизительно ( приблизно)

Объяснение:

нужно вычислить приближеное значение

Answer 2

Let's break down the expression step by step:

1. sin(32°)sin(148°): Using the product-to-sum trigonometric identity, we have:

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sin(A)sin(B) = (1/2)[cos(A-B) - cos(A+B)]

Substituting A = 32° and B = 148°:

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sin(32°)sin(148°) = (1/2)[cos(32° - 148°) - cos(32° + 148°)]
                   = (1/2)[cos(-116°) - cos(180°)]
                   = (1/2)[cos(116°) + cos(180°)]

Since cos(180°) = -1, we have:

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sin(32°)sin(148°) = (1/2)[cos(116°) - 1]

2. cos(32°)sin(302°): Using the same product-to-sum trigonometric identity:

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cos(A)sin(B) = (1/2)[sin(A+B) + sin(A-B)]

Substituting A = 32° and B = 302°:

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cos(32°)sin(302°) = (1/2)[sin(32° + 302°) + sin(32° - 302°)]
                   = (1/2)[sin(334°) + sin(-270°)]

Note that sin(-270°) is equal to -1, so:

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cos(32°)sin(302°) = (1/2)[sin(334°) - 1]

3. ctg(225°): Cotangent (ctg) is the reciprocal of the tangent function:

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ctg(A) = 1 / tan(A)

Substituting A = 225°:

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ctg(225°) = 1 / tan(225°)
          = 1 / (-1)
          = -1

Now, let's substitute the values we've calculated back into the original expression:

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sin(32°)sin(148°) - cos(32°)sin(302°) + ctg(225°)
= (1/2)[cos(116°) - 1] - (1/2)[sin(334°) - 1] - 1

Combine like terms:

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= (1/2)cos(116°) - (1/2)sin(334°) - (1/2) - 1

And calculate the trigonometric values:

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≈ 0.5009 - (-0.5009) - 0.5 - 1
≈ 0.5009 + 0.5009 - 0.5 - 1
≈ 0.5018 - 1.5
≈ -0.9982

So, the value of the expression is approximately -0.9982.