Question

Sin(2x-П\6)=-1 тригонометрия ​

Answer 1

$sin(2x-\frac{\pi }{6} )=-1\\\\2x-\frac{\pi }{6} =\frac{3\pi }{2} +2k\pi \\\\2x=\frac{3\pi }{2} +\frac{\pi }{6} +2k\pi\\ \\2x=\frac{5\pi }{3} +2k\pi \\\\x=\frac{5\pi }{6} +k\pi$

Answer 2

To solve the trigonometric equation sin(2x - π/6) = -1, we need to find the values of x that satisfy the equation. Remember that the sine function takes values between -1 and 1 for all real numbers.

First, let's find the general solution for the equation:

sin(2x - π/6) = -1

To find the general solution, we set 2x - π/6 equal to the angle whose sine is -1. This angle is -π/2 (or -90 degrees).

So we have:

2x - π/6 = -π/2

Now, isolate x:

2x = -π/2 + π/6

2x = -π/2 + 1/6π

2x = -3π/6 + 1/6π

2x = -2π/6

x = -π/6

Now, to find additional solutions, we can add integer multiples of the period of the sine function to the value of x. The period of sin(2x) is π, which means we can add integer multiples of π to the value of x.

The general solution is:

x = -π/6 + kπ

where k is an integer (positive, negative, or zero).

For example, for k = 0:

x = -π/6

For k = 1:

x = -π/6 + π = 5π/6

For k = -1:

x = -π/6 - π = -7π/6

And so on for other integer values of k. Each value of k gives a unique solution for x that satisfies the equation sin(2x - π/6) = -1.