![jellybooooo7446](/avatars/20988.jpg)
jellybooooo7446
21.07.2019 •
Mathematics
Can someone me in this trig question, ?a person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. what is the exact value of the position of the rider after the carousel rotates 5pi/12
Solved
Show answers
More tips
- F Family and Home Why Having Pets at Home is Good for Your Health...
- H Health and Medicine How to perform artificial respiration?...
- H Health and Medicine 10 Tips for Avoiding Vitamin Deficiency...
- F Food and Cooking How to Properly Cook Buckwheat?...
- F Food and Cooking How Many Grams Are In a Tablespoon?...
- L Leisure and Entertainment Carving: History and Techniques for Creating Vegetable and Fruit Decorations...
- P Photography and Videography How to Choose the Perfect Photo Paper for Your Images?...
- H Health and Medicine What vaccines do children need?...
- H Health and Medicine Reasons for the Appearance of Warts: Everything You Need to Know...
- A Art and Culture How to Learn Screaming: Step-by-Step Guide for Beginners...
Answers on questions: Mathematics
- M Mathematics Based on these boxplots, which of the following is true ? (5 points) The median rating for website B is greater than for website A. The interquartile range for website...
- M Mathematics Write an inequality and solve the problem. The difference of a number and –6 is less than 9....
- E English Read about the history if the vocabulary words. use 5e bold faced clues to write the vocabulary word that fits. then write what each word means now...
Ответ:
The exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).
The positionSince the position of the carousel is (x, y) = (20cosθ, 20sinθ) and we need to find the position when θ = 5π/12 = 5π/12 × 180 = 75°
So, substituting the value of θ into the positions, we have
(20cos75°, 20sin75°)
The value of 20cos75°20cos75° = 20cos(45 + 30)
Using the compound angle formula
cos(A + B) = cosAcosB - sinAsinB
With A = 45 and B = 30
cos(45 + 30) = cos45cos30 - sin45sin30
= 1/√2 × √3/2 - 1/√2 × 1/2
= 1/2√2(√3 - 1)
= 1/2√2(√3 - 1) × √2/√2
= √2(√3 - 1)/4
= (√6 - √2)/4
= (-√2 + √6)/4
So, 20cos75° = 20 × (-√2 + √6)/4
= 5 (-√2 + √6)
The value of 20sin75°20sin75° = sin(45 + 30)
Using the compound angle formula
sin(A + B) = sinAcosB + cosAsinB
With A = 45 and B = 30
sin(45 + 30) = sin45cos30 + cos45sin30
= 1/√2 × √3/2 + 1/√2 × 1/2
= 1/2√2(√3 + 1)
= 1/2√2(√3 + 1) × √2/√2
= √2(√3 + 1)/4
= (√6 + √2)/4
= (√2 + √6)/4
So, 20sin75° = 20 × (√2 + √6)/4
= 5(√2 + √6)
Thus, (20cos75°, 20sin75°) = 5 (-√2 + √6), 5(√2 + √6).
So, the exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).
Learn more about position here:
link
Ответ:
Ответ:
x-1 multiple 2x-1 = f(-x)