Question

Use the graph below to answer the question that follows:

trig graph with points at 0, 0 and pi over 2, 3 and pi, 0 and 3 pi over 2, negative 3 and 2 pi, 0 and 5 pi over 2, 3 and 3 pi, 0

What trigonometric function represents the graph?

f(x) = −3 sin(x − pi over 2)
f(x) = −3 cos(x − pi over 2)
f(x) = 3 cos(x − pi over 2)
f(x) = 3 sin(x − pi over 2)

Answer 1

Note that the graph contains the point
`\displaystyle{ ( ( \pi )/(2), 3)`

The 3 comes from the multiplication of the y-value in the parent function by.

Not considering the multiplication by 3 we would have
`\displaystyle{ (( \pi)/(2),1)`. Also remember that the available functions are
sin(x-π/2) and cos(x-π/2).

We can check that at π/2, sin(x-π/2) is sin(π/2-π/2)=sin(0)=0,

and, π/2, cos(x-π/2) is cos(π/2-π/2)=cos(0)=1.


Thus, our function is f(x)=3cos(x-π/2).

Check for π rad: f(π)=3cos(π-π/2)=3cos(π/2)=3*0=0.
and so on...

Answer: f(x) = 3 cos(x − pi over 2)