Question

Записать суммы в виде произведения: Sin10°+Cos70° = ...

Answer 1

$\sin(10) + \cos(70) = .....$

cos70° = cos ( 90° - 20° ) = sin 20°

$\sin(10) + \cos(70) = \sin(10) + \sin(20)$

Воспользуемся формулой:

$\sin( \alpha ) + \sin( \beta ) = 2 \sin(( \alpha + \beta ) \div 2) \cos(( \alpha - \beta ) \div 2)$

$\sin(10) + \sin(20) = 2 \sin(15) \times \cos(5)$

Answer 2

To express the sum Sin 10° + Cos 70° as a product, we can use the trigonometric identity:

Sin(a) + Cos(b) = 2 * Sin((a + b) / 2) * Cos((a - b) / 2)

So, for Sin 10° + Cos 70°:

a = 10° b = 70°

Let's plug these values into the formula:

Sin 10° + Cos 70° = 2 * Sin((10° + 70°) / 2) * Cos((10° - 70°) / 2)

Now, calculate the values inside the trig functions:

(10° + 70°) / 2 = 80° / 2 = 40° (10° - 70°) / 2 = -60° / 2 = -30°

Sin 40° ≈ 0.64279 (rounded to five decimal places) Cos -30° ≈ 0.86603 (rounded to five decimal places)

Now, substitute these values back into the formula:

Sin 10° + Cos 70° ≈ 2 * 0.64279 * 0.86603

Calculate the result:

Sin 10° + Cos 70° ≈ 1.11316 (rounded to five decimal places)

So, the expression Sin 10° + Cos 70° can be approximated as 1.11316 when rounded to five decimal places.