Sin x - cos x 0 0?

Answer 1

sin x - cos x = 0

sin x = cos x

(sin x)^2 = (cos x)^2

(sin x)^2 = 1 - (sin x)^2

2(sin x)^2 = 1

(sin x)^2 = 1/2

sin x = ± √(1/2)

sin x = ± (1/√2)

sin x = ± (1/√2)(√2/√2)

sin x = ± √2/2

x = ± pi/4 (± 45 degrees)

Any multiple of 2pi can be added to these values and sine (also cosine) is still ± √2/2. Thus all solutions of sin x - cos x = 0 or sin x = cos x are given by

x = ± pi/4 ± 2npi, where n is any integer.

By choosing any two integers , such as n = 0, n = 1, n = 2 we can find some solutions of sin x - cos x = 0.

n = 0, x = ± pi/4 ± (2)(n)(pi) = ± pi/4 ± (2)(0)(pi) = ± pi/4 ± 0 = ± pi/4

n = 1, x = ± pi/4 ± (2)(n)(pi) = ± pi/4 ± (2)(1)(pi) = ± pi/4 ± 2pi = ± 9pi/4

n = 2, x = ± pi/4 ± (2)(n)(pi) = ± pi/4 ± (2)(2)(pi) = ± pi/4 ± 4pi = ± 17pi/4