Related Rates: Trig Homework Solving x when Theta Increases

In summary: Here is where I am a little confused, I get cos(theta) = (5/2)√(3)/5 based off of the 30 60 90 triangle."So, you are trying to find the cosine of theta using the 30 60 90 triangle? If so, what is the value of the cosine of theta using the given information?
  • #1
kLPantera
43
0

Homework Statement



If theta increases at a constant rate of 3 radians per minute, at what rate is x increasing in units per measure at the instant when x equals 3 units?

The Attempt at a Solution



I drew the triangle and I came to the conclusion that I needed to use 5sin(theta)=x

Then I did the derivative and it comes out to 5cos(theta)d(theta)/dt=dx/dt

Here is where I am a little confused, I get cos(theta) = (5/2)√(3)/5 based off of the 30 60 90 triangle.

Am I doing this right? After I do the calculations, I don't get the right answer because no where are you supposed to have a sqrt in the answer.
 
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  • #2
kLPantera said:

Homework Statement



If theta increases at a constant rate of 3 radians per minute, at what rate is x increasing in units per measure at the instant when x equals 3 units?

The Attempt at a Solution



I drew the triangle and I came to the conclusion that I needed to use 5sin(theta)=x

Then I did the derivative and it comes out to 5cos(theta)d(theta)/dt=dx/dt

Here is where I am a little confused, I get cos(theta) = (5/2)√(3)/5 based off of the 30 60 90 triangle.

Am I doing this right? After I do the calculations, I don't get the right answer because no where are you supposed to have a sqrt in the answer.
Please write the complete problem as it was given to you.

I may be able to guess what you're supposed to do, but if my guess is wrong, that won't really help you.
 
  • #3
I typed the problem word for word, I'll include the multiple choice answers in this post:

a) 3
b) 15/4
c)4
d)9
e)12
 
  • #4
This is a related rates problem right? What is dθ/dt? What is dx/dt? Write down all your variables BEFORE you start trying to manipulate things.
 
  • #5
kLPantera said:
I typed the problem word for word, I'll include the multiple choice answers in this post:

a) 3
b) 15/4
c)4
d)9
e)12
If you typed it word for word, as follows, copied & pasted directly from your Original Post, & shown below:
"If theta increases at a constant rate of 3 radians per minute, at what rate is x increasing in units per measure at the instant when x equals 3 units?"​
then, where does the triangle come from, about which you stated:
"I drew the triangle and I came to the conclusion that I needed to use 5sin(theta)=x"​
??
 

What is the concept of related rates in trigonometry?

The concept of related rates in trigonometry involves finding the rate of change of one variable with respect to another variable. In this case, we are trying to find the rate at which the angle (theta) is increasing, while the value of x is also changing.

How do I solve for x when theta increases in a trigonometry problem?

To solve for x when theta increases, we can use the chain rule and implicit differentiation to find the derivative of the trigonometric equation. Then, we can plug in the given values for the rate of change of theta and solve for the rate of change of x.

Can I use the Pythagorean theorem to solve related rates problems in trigonometry?

Yes, the Pythagorean theorem is a useful tool in solving related rates problems in trigonometry. It can help us relate the different variables in the equation and make it easier to find their rates of change.

What are some tips for solving related rates problems in trigonometry?

Some tips for solving related rates problems in trigonometry include drawing a diagram to help visualize the problem, identifying the variables and their rates of change, using the given information to set up an equation, and carefully differentiating the equation to find the rates of change.

Are there any real-life applications of related rates in trigonometry?

Yes, related rates in trigonometry have many real-life applications, such as in physics, engineering, and astronomy. For example, it can be used to calculate the rate at which the angle of a satellite changes as it orbits the Earth, or the rate at which the sides of a building expand or contract due to temperature changes.

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