Question

-2sin(x+n/4)=корень 3

Answer 1

-2sin(x+π/4)=√3

sin(x+π/4)=√3/2

x+π/4=π/3+2πn

x+π/4=2π/3+2πn

x=π/3-π/4+2πn

x=2π/3-π/4+2πn

x=π/12+2πn

x=5π/12+2πn, n принадл. Z.

Answer 2

To solve the equation, we'll need to find the value of 'x' that satisfies the equation:

-2sin(x + n/4) = √3

To do this, we need to isolate 'sin(x + n/4)' first and then solve for 'x'. Here's how we can proceed:

Step 1: Divide both sides by -2:

sin(x + n/4) = -√3/2

Step 2: Recall the unit circle trigonometric values for sin:

sin(π/3) = √3/2 and sin(5π/3) = -√3/2

Step 3: We can find the possible values for (x + n/4) by comparing sin(x + n/4) with the unit circle values:

x + n/4 = π/3 + 2πk (where k is an integer) x + n/4 = 5π/3 + 2πm (where m is an integer)

Step 4: Solve for 'x' in each case:

Case 1: x = π/3 - n/4 + 2πk (where k is an integer)

Case 2: x = 5π/3 - n/4 + 2πm (where m is an integer)

So, there are infinite solutions for 'x' depending on the values of 'n', 'k', and 'm'. If you have specific values for 'n', 'k', or 'm', you can substitute them in the equations above to find the corresponding values of 'x'.