Trigonometric Functions- Grade 11

In summary, the first question deals with converting an angle of 350 degrees to radians, which simplifies to 35pi/18 radians. The second question involves determining the height of a passenger on a ferris wheel at a given time, with a function of h=20sin(pie/20(t-10))+21. After realizing a mistake in the phase, the correct equation is h=20sin(pie/20(t+10))+21. The follow-up question asks for the passenger's height after 15 seconds, which would be approximately 6.858 meters.
  • #1
majinknight
53
0
Ok I have two questions both i have done but not 100% sure I have done them correct. I am good with math but not so well at Trigonemetric stuff. Ok here it is.

1) Convert the following angles to radian measure, leave in simpilest rational form. 350 degrees.
Ok what i have done is this:
350pie/180
35pie/18 radians. Is that correct and simpilest form?

2) A ferris wheel with a radius of 20m rotates once every 40 seconds. At the bottom of the ride, the passenger is 1m above the ground. a) Determine a function that represents height, h, above ground and at time t, if h=41 at t=0.

Ok so i went and drew a graph of what i think it would looks like and from it got this information. Verticle translation of 21, phase shift of 10 to the right, amplitude of 20, period is 40 which equals pie/20. So from this I got the equation to be:
h=20sinpie/20(t-10)+21

Would this be correct for that question?

The follow up question part b) is Determine the passenger's height above the ground after 15 seconds. So i just took 15 and put it into my equation as t and got an answer of 35.142m. Did I do this correct and get the correct answer? Thank you very much it is much appreciated.
 
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  • #2
1) Looks good to me.

2) If you calculate h for t=0 you won't get 41 so your formula isn't correct (phase is wrong). That would also make your followup answer incorrect. I would use the cosine because the formula would be a bit simpler.

Doug
 
  • #3
Oh well the problem is i don't know what i have done wrong so that is where i get stuck, i wasnt sure if it looked right and this is one thing i am not very good at so any help would be appricated.
 
  • #4
You shouldn't give up so easily. Unless you haven't figured it out after a couple of weeks like a certain fundamental problem I have been working on. Also, I'm not sure why you say you are not very good at this. You have everything in this problem exactly right except for one thing, the phase. Like I said before.

If you are going into the physical sciences or engineering you will see this kind of problem appear on a regular basis so it is a good idea to learn to do it well now.

Once you have your function it is always a good idea to check it for a few values of t. Because this one is periodic, the beginning and the middle of the period are good choices. Because the period is 40 seconds, you should check the function for t=0 and t=20. The problem states that h=41 at t=0. Thus h=1 at t=20. Your function gives h=1 at t=0 and h=41 at t=20. This is exactly the opposite of what you want. This means the phase if off by [tex]\pi[/tex] radians. You have the sign of the phase wrong.

When you looked at the graph of [tex]sin(\theta)[/tex] you noticed that it is at maximum when [tex]\theta=\pi/2[/tex]. You probably reasoned that you needed to compensate with a phase of [tex]-\pi/2[/tex] where the phase you chose should have been [tex]\pi/2[/tex]. So, if your equation of motion is:

[tex]h=Asin({\omega}t+\theta)+c[/tex]

you correctly chose:

[tex]A=20, \omega=\frac{2\pi}{40}, c=21[/tex]

but chose:

[tex]\theta=-\frac{\pi}{2}[/tex]

instead of

[tex]\theta=\frac{\pi}{2}[/tex]

So your resulting equation should be:

[tex]h=20sin(\frac{2\pi}{40}t+\frac{\pi}{2})+21=20sin(\frac{\pi}{20}(t+10))+21[/tex]

Lecture over.

Doug
 
  • #5
Oh ok you i had tried and checked if it would worked befour and got an answer of 1 but thought i might had put a calculator error. Ok so i just had the sign wrong. Thanks for the help as that makes more sence. So than if the time was 15 seconds using the formula you would get approximently 6.858 correct?
 
Last edited:
  • #6
Yep.

Doug
 

1. What are trigonometric functions?

Trigonometric functions are mathematical functions that relate angles and sides of a right triangle. They include sine, cosine, tangent, cotangent, secant, and cosecant, and are commonly used in geometry and calculus.

2. How do you use trigonometric functions?

Trigonometric functions are used to solve problems involving right triangles, such as finding missing sides or angles. They can also be used to model periodic phenomena, such as sound waves or planetary orbits.

3. What is the unit circle and how is it related to trigonometric functions?

The unit circle is a circle with a radius of 1 centered at the origin on a Cartesian coordinate system. It is used to define the values of trigonometric functions for any angle, as the coordinates of a point on the unit circle correspond to the values of the trigonometric functions for that angle.

4. What is the difference between sine, cosine, and tangent?

Sine (sin), cosine (cos), and tangent (tan) are all trigonometric functions, but they represent different ratios of sides in a right triangle. Sine is the ratio of the opposite side to the hypotenuse, cosine is the ratio of the adjacent side to the hypotenuse, and tangent is the ratio of the opposite side to the adjacent side.

5. How do you solve trigonometric equations?

To solve a trigonometric equation, you must use the properties of trigonometric functions and algebraic techniques to isolate the variable. You may also need to use identities, such as the Pythagorean identity, to simplify the equation. Once the variable is isolated, you can use a calculator or reference table to find the solution in terms of angles or decimal approximations.

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