Apply trigonometric methods in solving problems

[Elara]

Hey, I was just wondering if someone could look this over and see if I've done it right because I'm unsure.

Find the period of time when it is safe to cross the inlet.

INFORMATION
- For an average tide assume that the water is 2 metres deep at high tide and 0.2 metres deep at low tide
- There are 12.5 hours between consecutive high tides. It is considered safe to walk across the inlet
when the depth of the water is less than 0.8 metres.

d(t)=a sin b (x-c) + d or d(t)=a cos b (x-c) + d
a=0.9
b=4pi/25
c= Points from graph (3.8 and 8.7) (I drew a graph)
d= 1.1

0.9 cos (4/25)t+1.1=0.8
0.9 cos (4/25)t=0.8-1.1
0.9 cos (4/25)t=-0.3
cos (4/25)t=-1/3
(4/25)t=arccosine(-13)
t=(arccosine(-1/3)) / 4 / 25
t=3.8

8.7-3.8=4.9hours

 

[blamocur]

I believe your answer is correct, but your intermediate steps are very confusing: you drop 'pi' from your formulae, and instead of "(arccosine(-1/3)) / 4 / 25" you most likely meant "(arccosine(-1/3)) / (4 / 25)".

 

[Elara]

I believe your answer is correct, but your intermediate steps are very confusing: you drop 'pi' from your formulae, and instead of "(arccosine(-1/3)) / 4 / 25" you most likely meant "(arccosine(-1/3)) / (4 / 25)".

Yea I did, and I was copying and pasting it so the pi just didnt show up, think you so much

 

[Cubist]

I agree with @blamocur that your answer is correct, well done !

c= Points from graph (3.8 and 8.7) (I drew a graph)

Here's the graph...



c1≈3.8 and c2≈8.7

0.9 cos (4/25)t+1.1=0.8

In addition to the comments in post#2, please show the above as...
0.9 cos(4*pi*t/25) + 1.1 = 0.8
or
0.9 cos((4/25)*pi*t) + 1.1 = 0.8
or similar, because this makes it more obvious that "t" is included in the expression passed to cos()

Note you can post an image of your written work if that's easier for you

Question for the other helpers
Is it OK to use "d" for a function and also use "d" for a numerical constant in the same question? Personally I'd prefer to see a different letter used (even though the difference is obvious in this question with the consistent use of "d(t)" for the function)

 

[topsquark]

Question for the other helpers
Is it OK to use "d" for a function and also use "d" for a numerical constant in the same question? Personally I'd prefer to see a different letter used (even though the difference is obvious in this question with the consistent use of "d(t)" for the function)

I don't usually recommend using the same variable symbol but so long as you make sure to use d(t) vs. d there should be no confusion. If you started to use notation like [imath]d: \mathbb{R} \to \mathbb{R}[/imath] or something then I would say no.

I forget who said it but I quote it to my Physics students who complain when I start using Greek variables:
"Life is short and the alphabet shorter."

-Dan

 

[Elara]

I agree with @blamocur that your answer is correct, well done !



Here's the graph...

View attachment 34089

c1≈3.8 and c2≈8.7


In addition to the comments in post#2, please show the above as...
0.9 cos(4*pi*t/25) + 1.1 = 0.8
or
0.9 cos((4/25)*pi*t) + 1.1 = 0.8
or similar, because this makes it more obvious that "t" is included in the expression passed to cos()

Note you can post an image of your written work if that's easier for you

Question for the other helpers
Is it OK to use "d" for a function and also use "d" for a numerical constant in the same question? Personally I'd prefer to see a different letter used (even though the difference is obvious in this question with the consistent use of "d(t)" for the function)

Hey, can you tell me where you made this graph? Thanks

 

[mmm4444bot]

Hello. Google keywords free equation graphs. The first listing is Desmos. There are others; some plotters are very basic.

In fact, if you google plot y=0.9*cos(4*pi*x/25)+1.1, you'll get a basic (zoomable, draggable) graph.

?
[imath]\;[/imath]

 

[Deleted member 4993]

Is it OK to use "d" for a function and also use "d" for a numerical constant in the same question?

Most of you know that in Physics, "distance travelled" or arc length) is generally indicated by 's'.

 

[Cubist]

Hey, can you tell me where you made this graph? Thanks

I grabbed a screenshot from the output of a graphing tool (see post #7). And then I used a "raster graphics editor" (called GIMP) to add some extra text, lines and labels. GIMP has a steep learning curve for a beginner therefore you might want to look for an easy image editing app to do any adjustments.