Trigonometric Equation problem

In summary, the question is to write a trigonometric equation that models the height of the top of the hour hand above the floor, with given variables and an image provided. The equation should be in the form of either h=A sinB(t+c)+D or h=A cosB (t+C)+D, with a period of 12 hours and a frequency of pi/6. The key to solving the problem is to figure out the height of the hand at 3 o'clock, which will give the average height of the graph. Drawing triangles can also help in solving the problem. The correct equation is h=28sin(pi/6)t +170.8, with help from a friend.
  • #1
XxDoiraxX
3
0
I'm stuck on a question from my calculus homework...T_T
Here's the question...
There is a large clock at the front of the lounge on the paddle steamer. The hour hand is 28 cm long and takes 12 hours to rotate once. At 2 o'clock the tip of the hour hand is 195 cm above the floor.

There's no equation given instead there's an image... (please view attachment for the image given)

The question is write a trigonometric equation that will model the height of the top of the hour hand above the floor. Where h = the height above the floor in centimetres, t = time since 12 O'clock in hours and the angel is measured in radians.

What I do know is that it must either be a cos or sin graph...
So must be in the form of h=A sinB(t+c)+D or h=A cosB (t+C)+D

I think the period is 12 hours...therefore if it is 12 hours the frequency must be pi divided by 6.

I don't understand how to work out the rest though...

please help?
 

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  • #2
Well, take what you know and apply it. First, you need to figure out how high the hand is at 3 o clock. That will give you the average height of the graph... and then work from there. I suggest first drawing a few triangles of what you know.
 
  • #3
Char. Limit said:
Well, take what you know and apply it. First, you need to figure out how high the hand is at 3 o clock. That will give you the average height of the graph... and then work from there. I suggest first drawing a few triangles of what you know.

At 3 O'clock?? I don't understand
 
  • #4
It's okay now ^^
I understand the question now :P
the equation is h=28sin(pi/6)t +170.8
got help from a friend xD
 

1. What is a trigonometric equation problem?

A trigonometric equation problem is an algebraic equation that involves trigonometric functions such as sine, cosine, tangent, etc. These equations can be solved using various trigonometric identities and techniques.

2. How do you solve a trigonometric equation problem?

To solve a trigonometric equation problem, you first need to simplify the equation using trigonometric identities. Then, use algebraic methods such as factoring or substitution to isolate the variable. Finally, check your solution by plugging it back into the original equation.

3. What are some common trigonometric identities used to solve equations?

Some common trigonometric identities used to solve equations include the Pythagorean identities, double angle identities, half-angle identities, and sum and difference identities. These identities can help simplify the equations and make them easier to solve.

4. What are some tips for solving trigonometric equation problems?

Here are some tips for solving trigonometric equation problems:
- Familiarize yourself with the trigonometric identities and formulas
- Isolate the variable using algebraic methods
- Use reference angles to help solve equations involving trigonometric functions
- Check your solutions by plugging them back into the original equation
- Practice, practice, practice!

5. Are there any online resources or tools available for solving trigonometric equation problems?

Yes, there are many online resources and tools available for solving trigonometric equation problems. These include equation solvers, step-by-step guides, and practice problems with solutions. Some examples include Wolfram Alpha, Mathway, and Khan Academy.

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