Equation using sin and cos

Question

x1 y1

0 55

15 35

30 10

45 35

60 55

75 35

90 10

105 35

120 55

What numbers need to be changed in this relationship in order to make two equations for this relationship one using sin and one using cos

Answer 1

Luhan:

Use radians instead of degrees. You need to change f(x) =55 to f(x) =60

degrees radians f(x)

0 0 60

15 π/12 35

30 π/6 10

45 π/4 35

60 π/3 60

75 5π/12 35

90 π/2 10

105 7π/12 35

120 2π/3 60

We can write the equation in the form f(x) = A*cos(ω(x-B))+C

A (amplitude) = (60-10)/2 = 25

period = 2π/ω The period is π/3 since f(0) = 60 f(π/3) =60 f(2π/3) =60

solving for ω, ω = 6

There is no horizontal offset. The graph reaches a maximum value at x=0 just like the standard cos() function.

C = (60+10)/2 = 35

We get f(x) = 25*cos(6x) + 35

I'll let you do the sin() function; There will be an offset of π/12 so B = π/12 for the sin()