Write equations of cosine functions using properties

Question

Find an equation for a sinusoidal function that has period 2​𝜋, amplitude 1, and contains the point (𝜋,4)

Cos

2pi/2pi=1

Cos(x)

4 = Cos(pi+C)+D

4= Cos (pi+0) +D

4= Cos (pi)+D

4= (-1) +D My misunderstanding is how to arrive at -1 ???

5= D

Cos(x)+5

.

Answer 1

Any function of the form y = cosx + C has amplitude 1 and period 2π.

Since (π, 4) is on the graph, we have 4 = cosπ + C.

So, 4 = -1 + C. Therefore, C = 5. Note: cosπ = cos180° = -1

So, the function is y = cosx + 5.