Question

1).cosx=12). cosx/2=13). cos(2x-π\3)=04). cos(π\4 -3πx)=1​

Answer 1

Ответ:

1) ответ

Объяснение:

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Answer 2

To find the solutions for each of these trigonometric equations, we'll use various trigonometric identities and techniques. Let's solve them one by one:

1. cos(x) = 0 To solve for x, set cos(x) equal to 0: cos(x) = 0

Now, find the values of x: x = π/2 + πn, where n is an integer.

2. cos(x/2) = 1/2 To solve for x, use the inverse cosine function: x/2 = π/3 + 2πn or x/2 = -π/3 + 2πn

Now, find the values of x: x = 2π/3 + 4πn or x = -2π/3 + 4πn, where n is an integer.

3. cos(2x - π/3) = 0 To solve for x, set cos(2x - π/3) equal to 0: cos(2x - π/3) = 0

Now, find the values of x: 2x - π/3 = π/2 + πn or 2x - π/3 = -π/2 + πn

Solve for x: 2x = π/2 + πn + π/3 or 2x = -π/2 + πn + π/3

x = (π/2 + πn + π/3)/2 or x = (-π/2 + πn + π/3)/2, where n is an integer.

4. cos(π/4 - 3πx) = 1 To solve for x, set cos(π/4 - 3πx) equal to 1: cos(π/4 - 3πx) = 1

Now, find the values of x: π/4 - 3πx = 2πn, where n is an integer.

Solve for x: -3πx = 2πn - π/4

x = (2πn - π/4)/(-3π), where n is an integer.

These are the solutions for the given trigonometric equations. Keep in mind that n can be any integer, so these equations have an infinite number of solutions.