Deck 6: Applications of Trigonometry

Question 1

A golf ball is hit with an initial velocity of 150 ft/sec at an angle of 29° from the horizontal. How long is the ball in the air?

Answer 1

4.55 seconds

Question 2

Draw the graph of

Answer 2

Question 3

Point A has rectangular coordinates (-4,4) . What are two sets of polar coordinates for point A , where ?

Answer 3

Question 4

Eliminate the parameter from the curve C defined by the parametric equations

Question 5

Find the angle between

Question 6

Find the polar equation that corresponds to the graph below.

Question 7

A plane is flying on a bearing of east of north at 550 mph. Express the velocity of the plane as a vector. Assume that there is no wind.

Question 8

Write the polar equation in rectangular form.

Question 9

Identify the graph of the polar equation

A) cardioid
B) rose curve
C) limaçon with inner loop
D) dimpled limaçon
E) convex limaçon

Question 10

What is the vector projection of onto ?

Question 11

What is the work done in lifting a 45 -pound child 5 feet off the ground?

A) 9 foot-pounds
B) 9 pounds per foot
C) 225 foot-pounds
D) 225 pounds per foot

Question 12

Draw the graph of
(Make sure you label the scale on your graph.)

Question 13

What is the unit vector in the direction of

Question 14

Find the components of the vector with direction angle and length 5 .

Question 15

What is the parameterization of the line through the points (5,-4) and (2,6) ?

Question 16

Write the complex number

in standard form.

Question 17

Question 18

Find using De Moivre's theorem.

A)
B)
C)
D)
E)

Question 19

Find the fifth roots of unity.

Question 20

Which of the following vectors are orthogonal?

A)
B)
C)
D)

Question 21

Question 22

Question 23

The parametric equations and
where
represent what curve? What is the rectangular
form of this curve?

Question 24

An airplane is flying on a bearing of at 395 mph. A wind is blowing with a bearing of at 35 mph. Find the actual speed and direction of the plane and explain how you arrived at your answer.

Question 25

Find the unit vector in the direction of (7,-24) .

Question 26

Let A=(5,2), B=(-2,4) . Express the vector determined by as a linear combination of

Question 27

The scalar k is equal to 4. Vectors and are defined as
Evaluate

Question 28

Which parametric equations describe a spiral beginning at the origin for

A) x=t cos t and y=t sin t
B) x=t sin t and y=t sin t
C) x=5 cos t and y=5 sin t
D) x=cos t and y=sin t
E) x=t and y=sin t

Question 29

Evaluate
Express your answer in trigonometric form.

Question 30

What is the vector projection of onto

Question 31

An NFL punter at the 15 -yard line kicks a football with initial velocity of 90 feet per second at an angle of elevation of Let t be the elapsed time since the football is kicked.
(a) Write parametric equations that represent the distance the football travels. Assume that x=0 represents the 15 -yard line.
(b) What interval represents the possible values for t ?
(c) What is the distance the ball travels in feet downfield (to the nearest whole number)?

Question 32

Let A=(2,5), B=(-3,6) . Express the vector determined by as a linear combination of

Question 33

Determine the rectangular coordinates of the point with polar coordinates

Question 34

Find the unit vector in the direction of

Question 35

Question 36

An airplane is flying on a bearing of at 420 mph. A wind is blowing with a bearing of at 30 mph. Find the actual speed and direction of the plane and explain how you arrived at your answer.

Question 37

Let Find the vector v such that and

Question 38

Find the quotient for the complex numbers

and

Question 39

The scalar k is equal to 5 . Vectors and are defined as
and
Evaluate

Question 40

The locations, given in polar coordinates, of two planes approaching the Ontario airport are and
Find the distance between the planes.

Question 41

An NFL punter at the 15 -yard line kicks a football with initial velocity of 95 feet per second at an angle of elevation of Let t be the elapsed time since the football is kicked.
(a) Write parametric equations that represent the distance the football travels. Assume that x=0 represents the 15 -yard line.
(b) What interval represents the possible values for t ?
(c) What is the distance the ball travels in feet downfield (to the nearest whole number)?

Question 42

What is the vector projection of onto

Question 43

The locations, given in polar coordinates, of two planes approaching the Toronto airport are and Find the distance between the planes.

Question 44

Question 45

Evaluate
Express your answer in trigonometric form.

Question 46

Determine the rectangular coordinates of the point with polar coordinates

Question 47

Let
Find the vector v such that
and

Question 48

State the smallest
that gives a complete graph of the polar equation Sketch the graph and label the graph to show which petals are generated by positive values of r and which by negative values of r.

Question 49

Question 50

Find the quotient for the complex numbers
and

Question 51

Which parametric equations describe a circle with its center at the origin and a radius of 7 for

A) x=7 cos t and y=7 sin t
B) x=7 sin t and y=7 sin t
C) x=cos 7 t and y=sin 7 t
D)
E) x=49 cos t and y=49 sin t

Question 52

The parametric equations x(t)=t-2 and

represent what curve?
What is the rectangular form of this curve?