Question

9sinx-17cosx=Корень 370

Answer 1

Ответ:

в фотомафе вот так, но вы наверное это не проходили....

Answer 2

To find the value of x in the equation 9sin(x) - 17cos(x) = √370, we can use trigonometric identities and basic algebraic techniques.

Let's first simplify the equation:

9sin(x) - 17cos(x) = √370

We know the Pythagorean identity: sin^2(x) + cos^2(x) = 1

Divide the entire equation by √(9^2 + (-17)^2) = √370:

(9/√370)sin(x) - (17/√370)cos(x) = 1

Now, we need to find the values of sin(x) and cos(x) for which the equation holds true.

Let's use the concept of angles with respect to right triangles:

sin(θ) = opposite/hypotenuse cos(θ) = adjacent/hypotenuse

Let's assume we have a right triangle with an opposite side of 9, an adjacent side of -17, and a hypotenuse of √370.

Now, we can use the Pythagorean theorem to find the hypotenuse:

√(9^2 + (-17)^2) = √(81 + 289) = √370

So, we have a right triangle with sides: opposite = 9, adjacent = -17, and hypotenuse = √370.

Now, to find the value of θ (angle x), we can use the inverse trigonometric functions:

θ = arctan(opposite/adjacent) = arctan(9/-17)

Using a calculator, we find θ ≈ -27.32 degrees (approximately).

However, this is not the only solution, as trigonometric functions have periodicity. The sine and cosine functions have a period of 360 degrees (or 2π radians). So, we can add or subtract multiples of 360 degrees from our solution.

General solution:

θ = -27.32° + 360° * n, where n is an integer

So, the possible values of x are:

x ≈ -27.32° + 360° * n, where n is an integer

Keep in mind that there are infinite solutions for x that satisfy the given equation.