Question

1) sin2x= 2) 3)5sin3x-2cos3x=0 4) 5)2sin4x-3 ПОЖАЛУЙСТА РЕШИТЕ ДАЮ 80 БАЛОВ

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

1) To solve the equation sin(2x) = 0, we need to find the values of x that satisfy this equation.

The sine function is equal to zero at certain angles. In this case, we need to find the angles whose sine is zero. The sine function is zero at multiples of π (pi), so we can write the equation as:

2x = nπ, where n is an integer.

To find the values of x, we divide both sides of the equation by 2:

x = nπ/2, where n is an integer.

So the solutions to the equation sin(2x) = 0 are x = nπ/2, where n is an integer.

2) To solve the equation 5sin(3x) - 2cos(3x) = 0, we can use the trigonometric identity sin^2(x) + cos^2(x) = 1.

First, let's divide the equation by cos(3x):

5sin(3x)/cos(3x) - 2 = 0.

Using the identity sin(x)/cos(x) = tan(x), we can rewrite the equation as:

5tan(3x) - 2 = 0.

Now, let's solve for tan(3x):

5tan(3x) = 2.

tan(3x) = 2/5.

To find the values of x, we can take the inverse tangent (arctan) of both sides:

3x = arctan(2/5).

x = (1/3) * arctan(2/5).

So the solution to the equation 5sin(3x) - 2cos(3x) = 0 is x = (1/3) * arctan(2/5).

3) To solve the equation 2sin(4x) - 3 = 0, we isolate the sine term:

2sin(4x) = 3.

Dividing both sides by 2:

sin(4x) = 3/2.

However, the sine function only takes values between -1 and 1, so there are no solutions to this equation.

Therefore, the equation 2sin(4x) - 3 = 0 has no solutions.

Please note that the solutions provided are based on the given equations and standard trigonometric identities.