Arturo O. answered • 12/14/17

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Use the identity

sin(a + b) = sin(a) cos(b) + cos(a) sin(b)

Multiply and divide f(x) by the square root of the sum of the squares of the coefficients, which is √(1

^{2}+ 1^{2}) = √2f(x) = sin(x) + cos(x) = √2 [sin(x)(1/√2) + cos(x)(1/√2)]

1/√2 = cos(π/4) = sin(π/4) ⇒

f(x) = √2 [sin(x) cos(π/4) + cos(x) sin(π/4)]

f(x) = √2 sin(x + π/4) = Asin(bx + C)

**A = √2**

**B = 1**

**C = π/4**