Trigonometric functions ->sine function EASY

[Voltman123]

Trigonometric functions -->sine function EASY!

Homework Statement

Consider the trigonometric function f(t)=-1+4sin(0.5π(t-1)).
(a) What is the amplitude of f(t)?
(b) What is the period of f(t)?
(c) What are the maximum and minimum values attained by f(t)?

Homework Equations

Period: 2π/b

The Attempt at a Solution

The amplitude is 4.
The period is 2π/b = 2π/0.5 = 4π.

How do you find the maximum and minimum values?

Any help would be appreciated!

 

[Dick]

Homework Statement

Consider the trigonometric function f(t)=-1+4sin(0.5π(t-1)).
(a) What is the amplitude of f(t)?
(b) What is the period of f(t)?
(c) What are the maximum and minimum values attained by f(t)?

Homework Equations

Period: 2π/b

The Attempt at a Solution

The amplitude is 4.
The period is 2π/b = 2π/0.5 = 4π.

How do you find the maximum and minimum values?

Any help would be appreciated!

sin(x) varies between +1 and -1, right?

 

[SammyS]

The amplitude is 4.
The period is 2π/b = 2π/0.5 = 4π.

That period looks wrong to me.

 

[Dick]

That period looks wrong to me.

Good point. b is 0.5π, right?

 

[Voltman123]

sin(x) varies between +1 and -1, right?

How do we find the y intercept for this equation?

f(t)= -1+4sin(0.5π(t-1))
0=-1+4sin(0.5π(t-1))
1=4sin(0.5π(t-1))

How do I do the rest?

I know the y intercept is -5 but I'd like to know how you get there if you try to find it by hand.

 

[Voltman123]

Good point. b is 0.5π, right?

How is it 0.5π?

 

[HallsofIvy]

"b" was, in the first post, the coefficient of t in the general form.

Yes, "b" is 0.5\pi so the period is 2\pi/0.5\pi= 4, not "4\pi".

 

[Dick]

How do we find the y intercept for this equation?

f(t)= -1+4sin(0.5π(t-1))
0=-1+4sin(0.5π(t-1))
1=4sin(0.5π(t-1))

How do I do the rest?

I know the y intercept is -5 but I'd like to know how you get there if you try to find it by hand.

That's not really a 'y-intercept', you are finding the zeros of f(t). And since it's periodic there will be lots of them. For the rest you've got (1/4)=sin(0.5π(t-1)). Try and figure out where sin(x)=1/4. Set 0.5π(t-1) equal to those values.