149k views
1 vote
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)

1 Answer

4 votes
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)
User Tomasz Rozmus
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories