Question

1)sin (x/3+п/4)=02)cos(x/2-п/2)=1​

Answer 1

1)

$sin(\frac{x}{3} +\frac{\pi }{4} )=0 ,\\\frac{x}{3} +\frac{\pi }{4}=\pi n,\\\frac{x}{3} =-\frac{\pi }{4}+\pi n|*3\\x=-\frac{3\pi }{4}+3\pi n$,n∈Z

2)

$cos(\frac{x}{2} -\frac{\pi }{2} )=1\\\frac{x}{2} -\frac{\pi }{2}=2\pi n |*2\\x-\pi =4\pi n\\x=\pi +4\pi n$n∈Z

Answer 2

To solve these equations, we'll use the trigonometric identities and properties. Let's solve them one by one:

1. sin(x/3 + π/4) = 0

To find the values of x that satisfy this equation, we'll use the fact that sin(θ) = 0 when θ is an integer multiple of π.

x/3 + π/4 = nπ, where n is an integer.

x/3 = nπ - π/4

x = (3nπ - 3π/4) * 3

x = 3nπ - 9π/4

So, x can be expressed as x = (3nπ - 9π/4), where n is an integer.

2. cos(x/2 - π/2) = 1

To solve this equation, we'll use the fact that cos(θ) = 1 when θ is an even multiple of π.

x/2 - π/2 = 2nπ, where n is an integer.

x/2 = 2nπ + π/2

x = 4nπ + 2π

x = 2(2nπ + π)

So, x can be expressed as x = 2(2nπ + π), where n is an integer.

These are the general solutions to the given equations. Depending on the range or specific conditions of the problem, you may need to find solutions within a specific interval or domain.