A circle with a radius of 15.5 cm is drawn on a large piece of cardboard. A central angle of 65° is drawn. What is the length of the arc subtended by this angle, rounded to the nearest tenth of a cm?

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MATH 30-1

                                                            ASSIGNMENT# 6

1. Write the equation of a circle with the given radius, and its centre at (2, 3).

    3 units

2.  A circle with a radius of 15.5 cm is drawn on a large piece of cardboard. A central angle of 65° is drawn. What is the length of the arc subtended by this angle, rounded to the nearest tenth of a cm?

3. Find the angular velocity in radians per second of a point on a bicycle tire if it completes 5 revolutions in 3 seconds

4. A Ferris wheel with a radius of 12.5 m makes 5 rotations every minute.

a. Find the average angular speed of the wheel in radians/second

b. How far does a rider travel if the ride lasts for 3 minutes?

5. A vehicle has tires that are 75 cm in diameter. A point is marked on the edge of the tire. Determine the measure through which the point turns every second if the vehicle is travelling at 110km/h. Give your answer in radians and degree

6. The point D(-8, –13) lies on the terminal arm of an angle q in standard position. What is the exact value of each trigonometric ratio for θ

7. . If tan θ =  ( quadrant III) find the remaining trigonometric ratios. Show the diagram

8. .What is the exact value of csc

9.  If cot x =  - and sin x is positive, find the exact  value of cos x and sin x

10.  Determine the exact measure of the other five trigonometric ratios under the given conditions

                csc   = -     0 θ ≤ 360

11.  Given  in standard position with its terminal arm in the stated quadrant find the exact values of the remaining five trigonometric ratios.                                                                                               

sec = - ,                

12. Find the exact value of cos 7500 + sin

13.  In one cycle of a sinusoidal function, a maximum occurs at (3, 10) and a minimum occurs at (8, -2).  Find the equation of the function in the form y = a cos (b(x – c)) + d in radians

 

 

14. Find the domain, range, period, phase shift, amplitude and vertical displacement  of the following sine graph. Write the equation in the form y = a sin b(x-x) +d and y = a cosb(x- c) +d

15. At the bottom of its rotation, the tip of the blade on a windmill is 9 m above the ground. At the top of its rotation, the blade tip is 24 m above the ground. The blade rotates once every 5s.

  A bug is perched on the tip of the blade when the tip is at its lowest point.

a. Determine the cosine equation of the graph for the bug’s height over time?

b. What is the bug’s height after 4s?

c. For how long is the bug more than 17m above the ground?

16. The height, h in metres, above the ground of a rider on a Ferris wheel after t seconds can be modelled by the sine function h(t)  = 12 sin +15

a) Determine the maximum and the minimum height of the rider above the ground

b) Determine the time required by the rider to complete one revolution

c) Determine the height of the rider above the ground after 45 s   

17. The pendulum of a grandfather clock swings with a periodic motion that can be represented by a trigonometric function. At rest, the pendulum is 17 cm above the base. The highest point of the swing is
22 cm above the base, and it takes 2 s for the pendulum to swing back and forth once. Assume that the pendulum is released from its highest point.

a) Write a cosine equation that models the height of the pendulum as a function of time.

 

18.  Determine the exact measure of each angle.                                             

 a)  12 cos( 2(x - 450)) + 8 = 10 ,

b. sin2x = cos x – cos 2x,

c. 3 csc x-sin x =2,

d. . sin2x = 2cosx cos2x ,   

5. Simplify

a.

b.

c.

d.

3. What is the exact value of

a.

b. tan 1650

c. sin

19. Given  .What is the value of cos x

20. Prove

a.

b.

c)

d. Cos (3x) = 4 cos3( x) - 3 cos( x)

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