Melody

Yes that sounds right.

A softball pitcher winds up and spins her arm around before releasing the ball. The pitcher's shoulders are 1.35m tall and arm is 0.36m long. The pitcher can spin her arm 15 revolutions every 2 seconds and at t = 0 her hand is it it's maximum height.

A) Determine an sinusoidal equation to represent the height of the pitchers hand.

B) Determine the height of the pitchers hand at t = 0.1 seconds

Here is the equation.

\(\displaystyle h=Asin[2\pi f(t-p)]+v \)

h is height in metres

t is time in seconds

A is the amplitude                                                 A=0.36

v is the vertical shift                                               v= 1.35

f is the frequency which is  cycles/second            f=15/2

p is horizontal phase shift.  

    Here there are  2seconds per 15revolutions.  

     the phase shift is a quarter of that in a negative direction.  So p= -1/30

so

\(h= 0.36sin[2\pi*\frac{15}{2}(t+\frac{1}{30})]+1.35\\ h= 0.36sin[15\pi(t+\frac{1}{30})]+1.35\\\)

Here is the graph

Now you can check my working and answer the substitution questions yourself.

All looks good to me.

The question does say to the nearest 10th.

It seems you are learning very quickly.  Good for you.

Just memorize those formulas.

Have you done that already or would you like some memory hints?

Are you having a go at this one now Roxettna. ?

Yes that is good Roxettna except you presentation is just a little bit off.

AB^2   = 60^2+74^2-2(60)(74)cos(85)

AB^2  =3600+5476-8880*0.087155743

AB^2  =8302.057002

sqrt of 8302.057002  = 91.11 miles

so

AB = 91.11

The distance between the ships is approx 91 miles.

Since the other two distances are only written to the nearest mile, it makes sense that the third one would be good to the nearest whole mile as well.

But that does not matter.  91.11 miles is a good answer.   

This question has been asked and answered about a billion times.

It could equally well be - infinity. 

So I would call it undefined.

For starters you have not labeled  the sides of your triangle properly.

Side a  must be  opposite angle A

Same for b and c

Always little anglers for sides and the Capital equivalent for the opposite angle.

After that you will need to use sine  rule to get another angles

and then angle sum of a triangle to get the third one.

You can display what you do for each step if you want. People will give you feedback.   

You have uses Pythagoras's theorem.

This only works if the angle is 90 degrees,  Your angle is 48+37

You have to use the cosine rule to solve this.

Here is a tutorial on it if you need one.