Question

Which numbers complete the blanks when solving the equation cos(x+2pi)= -(square root of 2/2) over the interval [0, 2pi]?

Answer 1

A 1;0

Explanation:

Answer 2

1, 0

Explanation:

Let
`\cos (x+2\pi) = -(√(2))/(2)`. From Trigonometry we remember the following identity:

`\cos (a+b) = \cos a \cdot \cos b - \sin a \cdot \sin b` (Eq. 1)

Where
`a` and
`b` are angles measured in radians.

Then, we proceed to expand the given expression:

`\cos x \cdot \cos 2\pi - \sin x \cdot \sin 2\pi = -(√(2))/(2)`

`\cos x \cdot 1 - \sin x \cdot 0 = -(√(2))/(2)`

`\cos x = -(√(2))/(2)`

Therefore, correct answer is "1, 0".