Question

Sin37°⋅cos9°+cos37°⋅sin9°=

Answer 1

Ответ:

sin46° ≈ 0,7193398

Объяснение:

Применим тригонометрическое тождество

sin(α+β)=sinα·cosβ+cosα·sinβ.

Тогда при α=37° и β=9°:

sin37°⋅cos9°+cos37°⋅sin9° = sin(37°+9°) = sin46°.

Определим приблизительное значение:

sin46° ≈ 0,7193398

Answer 2

The given expression involves trigonometric functions and angles. Using trigonometric identities, we can simplify the expression:

sin(37°)⋅cos(9°) + cos(37°)⋅sin(9°)

We can use the sum-to-product identity for sine:

sin(A)⋅cos(B) + cos(A)⋅sin(B) = sin(A + B)

In this case, A = 37° and B = 9°, so:

sin(37°)⋅cos(9°) + cos(37°)⋅sin(9°) = sin(37° + 9°)

Adding the angles:

37° + 9° = 46°

So the simplified expression is:

sin(46°)

Now, if you calculate the sine of 46° using a calculator or trigonometric tables, you will get the value of approximately 0.7193. Therefore:

sin(37°)⋅cos(9°) + cos(37°)⋅sin(9°) ≈ 0.7193