Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Answer:
Refer to your notes from module 6 on this.
Step-by-step explanation:
Complete this test question just like you did the practice question from the module. Remember your test is an open note test, but it is not a copy from the internet test. You can do it!!!
The values of [tex]\theta[/tex] for different conditions were calculated with the help of trigonometric functions.
What are the solutions to trigonometric functions?
The solution of trigonometric functions is the values of angles where the function value becomes zero.
Given function is:
A)[tex]f(\theta ) = 2Sin\theta +\sqrt{3}[/tex]
[tex]f(\theta ) = 2Sin\theta +\sqrt{3} = 0\\2Sin\theta = -\sqrt{3} \\Sin\theta =-\frac{\sqrt{3} }{2}[/tex]
[tex]\theta =n\pi +\frac{\pi }{3}[/tex] where n=1,3,5,7......
So, at [tex]\theta =n\pi +\frac{\pi }{3}[/tex] pogo stick's spring will be equal to its non-compressed length.
B)If the angle was doubled, the function will look like this,
[tex]f(\theta ) = 2Sin2\theta +\sqrt{3}[/tex]
[tex]f(\theta ) = 2Sin2\theta +\sqrt{3} =0[/tex]
[tex]2Sin2\theta +\sqrt{3} = 0\\2Sin2\theta = -\sqrt{3} \\Sin2\theta =-\frac{\sqrt{3} }{2}[/tex]
[tex]2\theta =n\pi +\frac{\pi }{3}\\\theta = \frac{n\pi }{2} +\frac{\pi }{6}[/tex]where n=1,3,5,7....
if n=1, [tex]\theta =\frac{2\pi }{3}[/tex]
n=2, [tex]\theta =\frac{7\pi }{6}[/tex]
n=3, [tex]\theta =\frac{5\pi }{3}[/tex]
So, [tex]\theta =\frac{2\pi }{3}, \frac{7\pi }{6} ,\frac{5\pi }{3}[/tex] will be solution in [0,2π}.
C)[tex]g(\theta) =1-cos^{2} \theta +\sqrt{3}[/tex]
[tex]g(\theta) =Sin^{2} \theta + \sqrt{3}[/tex]
[tex]g(\theta) =f(\theta)[/tex]
[tex]sin^{2} \theta +\sqrt{3} = 2Sin\theta+\sqrt{3}[/tex]
[tex]Sin^2\theta = 2Sin\theta[/tex]
[tex]Sin^2\theta-2Sin\theta = 0\\Sin\theta(Sin\theta-2) =0\\Sin\theta =2(NotPOSSIBLE)\\Sin\theta =0[/tex]
[tex]\theta=n\pi[/tex] where n=1,2,3.....
So, [tex]\theta=n\pi[/tex], the lengths of springs from the original pogo stick and the toddler's pogo stick are equal.
Hence, the values of [tex]\theta[/tex] for different conditions were calculated with the help of trigonometric functions.
To get more about trigonometric functions visit:
https://brainly.com/question/2291993
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.