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This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 10-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 5 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. B B B al some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 5 cos(3πt) and y= 5 sin(3πt) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot (3лt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 5 cos(3πt) + 10 sin(3лt) (d) Express the slope of the rod as a function of t: -cot (3πt) (c) Find the first time when the rod is tangent to the circle: seconds. (d) At the time in (c), what is the slope of the rod? (e) Find the second time when the rod is tangent to the circle: seconds. (f) At the time in (e), what is the slope of the rod?

This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 10-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 5 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. B B B al some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 5 cos(3πt) and y= 5 sin(3πt) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot (3лt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 5 cos(3πt) + 10 sin(3лt) (d) Express the slope of the rod as a function of t: -cot (3πt) (c) Find the first time when the rod is tangent to the circle: seconds. (d) At the time in (c), what is the slope of the rod? (e) Find the second time when the rod is tangent to the circle: seconds. (f) At the time in (e), what is the slope of the rod?

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.4: Hyperbolas
Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
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This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 10-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 5 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. B B B al some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 5 cos(3πt) and y= 5 sin(3πt) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot (3лt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 5 cos(3πt) + 10 sin(3лt) (d) Express the slope of the rod as a function of t: -cot (3πt) (c) Find the first time when the rod is tangent to the circle: seconds. (d) At the time in (c), what is the slope of the rod? (e) Find the second time when the rod is tangent to the circle: seconds. (f) At the time in (e), what is the slope of the rod?
Transcribed Image Text:This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 10-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 5 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. B B B al some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 5 cos(3πt) and y= 5 sin(3πt) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot (3лt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 5 cos(3πt) + 10 sin(3лt) (d) Express the slope of the rod as a function of t: -cot (3πt) (c) Find the first time when the rod is tangent to the circle: seconds. (d) At the time in (c), what is the slope of the rod? (e) Find the second time when the rod is tangent to the circle: seconds. (f) At the time in (e), what is the slope of the rod?
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