# Homework Help: Trigonometric functions ->sine function EASY!

1. May 2, 2013

### Voltman123

Trigonometric functions -->sine function EASY!

1. The problem statement, all variables and given/known data
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)?

2. Relevant equations

Period: 2π/b

3. 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!

2. May 2, 2013

### Dick

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

3. May 2, 2013

### SammyS

Staff Emeritus
That period looks wrong to me.

4. May 2, 2013

### Dick

Good point. b is 0.5π, right?

5. May 3, 2013

### Voltman123

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.

6. May 3, 2013

### Voltman123

How is it 0.5π?

7. May 3, 2013

### 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 "$4\pi$".

8. May 3, 2013

### Dick

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.