Jo and Ashton are riding on two different Ferris wheels that are side by side. B

Question

Jo and Ashton are riding on two different Ferris wheels that are side by side. Both Ferris wheels have a radius of 25 feet, but one rotates three times as fast as the other. Jo, a thrill-seeker, is riding on the faster-rotating Ferris wheel while Ashton is riding on the slower one. They both begin their rides at the same time, starting from the 3 o'clock position. Ashton's Ferris wheel (the slower one) makes only one rotation before the ride stops. Let aa be the measure of the angle (in radians) that Ashton's seat sweeps out from the 3 o'clock position.

a. Define a function f that gives Ashton's vertical distance above the horizontal diameter in terms of a. Preview f(a) 25 sin(a 2a) syntax ok (a) 25sin(a+2a) b. Write an expression that gives the angle (in radians that Jo's seat sweeps out from the 3 o'clock position in terms of a Preview sin(3a) syntax ok sin(3a) c. Define a function h that gives Jo's vertical distance above the horizontal diameter in terms of a, the angle swept out by Ashton's seat (in radians). Preview h (a) 25 sin(3a) syntax ok hla) 25sin(3a) d. For which values of a will Jo and Ashton be at the same height? (Hint: write sin(3a) sin(a 2a), and use the sum formula for sine.) Preview e. Define a function g that gives Ashton's horizontal distance to the right of the vertical diameter in terms of a. Preview gla 5 cos(a 2a) sy lg(a) 25cosla 2a) f. Define a function k that gives Jo's horizontal distance to the right of the vertical diameter in terms of a Preview k(a) 25 cos(3a) syntax ok k(a) 25cos(3a) g. For which values of a will Jo and Ashton have the same horizontal distance to the right of the vertical diameter? (Hint: write cos(3a) (a 2a), and use the sum formula for cosine.) Preview h. Jo wants to Snapchat a picture of Ashton on the Ferris wheel. In order to do this, Jo and Ashton need to have the same vertical height and horizontal distance to the right of the center of the Ferris wheel. For what values of a will Jo be able to take the picture? Preview

Explanation / Answer

d) we have to find values of a for which Jo and Ashton be at the same height.

i.e. 25 sin(3a) = 25 sin(a+2a)

sin(3a)= sin(a+2a)

Using sum formula of sine

sin(3a)= sin(2a+a)

= sin2a.cosa + cos2asina

= 2sinacosa.cosa + (1-2sin2a)sina

= 3sina - 4sin3a.

Hence :

Sin3a = 3sina-4sin3a

a = 20°.

e) g(a)= 25 cos(a+2a)

f) k(a)= 25 cos3a

g) Jo and ashton have same horizontal distance:

25cos(a+2a)= 25 cos(3a)

Solving cos(3a) by cosine sum formula

Cos(3a) = cos(2a+a)

= cos(2a)cos(a)- sin(2a)sin(a)

=(2cos2a-1)cosa - 2sinacosa.sina

= 4cos3a- 3cosa

I.e. cos 3a = 4cos3a- 3 cosa

a = 40°.

h ) a= 20,40.

And you can use sin3a = sin(a+2a)

Cos3a= cos(a+2a)

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