Deck 6: Analytic Trigonometry

Question 1

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Answer 1

Question 2

Solve the given trigonometric equation exactly for all reals.

Answer 2

Question 3

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Answer 3

Question 4

Solve the given trigonometric equation exactly for all reals.

Question 5

Solve the given trigonometric equation exactly for all reals.

Question 6

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 7

Solve the given trigonometric equation exactly over the interval, -2π ≤ θ ≤ 2π.

Question 8

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 9

Solve the given trigonometric equation exactly for all reals.

Question 10

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 11

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 12

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 13

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 14

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 15

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 16

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 17

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 18

Solve the given trigonometric equation on 0° ≤ θ ≤ 360°, and express answer in degrees to two decimal places.

Question 19

Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

Question 20

Solve the given trigonometric equation on 0° ≤ θ ≤ 360°, and express answer in degrees to two decimal places.

Question 21

Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

Question 22

Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

Question 23

Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

Question 24

Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

Question 25

Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

Question 26

Solve the given trigonometric equation on 0° ≤ θ ≤ 360° and express answer in degrees to two decimal places.

Question 27

The monthly sales of soccer balls is approximated by
where x is the number of the month (January is x = 1, etc.) During which month do the sales reach 2346.4?

Question 28

The monthly sales of soccer balls is approximated by
where x is the number of the month (January is x = 1, etc.) During which two months do the sales reach 2200?

Question 29

The number of deer on an island is given by
where x is the number of years since 2000. During what year is it the first time after 2000 that the number of deer reaches 250?

Question 30

Solve the given trigonometric equation exactly over the interval, 0 $\le$ $\theta$ $\le$ 2 $\pi$ .

A)
B)
C)
D)

Question 31

Solve the given trigonometric equation exactly over the interval, 0 $\le$ $\theta$ $\le$ 2 $\pi$ .

A)
B)
C)
D)

Question 32

Solve the given trigonometric equation exactly for all reals.

A)
B)
C)
D)

Question 33

Solve the given trigonometric equation exactly over the interval, 0 $\le$$\theta$$\le$ 2 $\pi$ .

A)
B)
C)
D)

Question 34

Solve the given trigonometric equation exactly for all reals.

A)
B)
C)
D)

Question 35

Solve the given trigonometric equation exactly over the interval, 0 $\le$ $\theta$ $\le$ 2 $\pi$ .

A)
B)
C)
D)

Question 36

Solve the given trigonometric equation exactly over the interval, 0 $\le$ $\theta$ $\le$ 2 $\pi$ .

A)
B)
C) ,
D) none of the above

Question 37

Solve the given trigonometric equation exactly over the interval, 0 $\le$ $\theta$ $\le$ 2 $\pi$ .

A)
B)
C)
D) none of the above

Question 38

Solve the given trigonometric equation exactly over the interval, 0 $\le$ $\theta$ $\le$ 2 $\pi$ .

A)
B)
C)
D)

Question 39

Solve the given trigonometric equation on 0° $\le$ $\theta$ $\le$ 360° and express answer in degrees to two decimal places.

A) 110.78^o, 159.22^o, 290.78^o, 339.22^o
B) 110.78^o, 159.22^o, 20.78^o, 69.22^o
C) 20.78^o, 69.22^o, 200.78^o, 249.22^o
D) 290.78^o, 339.22^o, 20.78^o, 69.22^o

Question 40

Solve the given trigonometric equation on 0° $\le$ $\theta$ $\le$ 360°and express answer in degrees to two decimal places.

A) 250.07^o
B) 125.04^o
C) 54.96^o
D) no solution

Question 41

Solve the given trigonometric equation on0° $\le$ $\theta$ $\le$ 360° and express answer in degrees to two decimal places.

A) 61.22^o
B) 30.61^o, 149.39^o
C) 210.61^o
D) no solution

Question 42

Solve the given trigonometric equation on0° $\le$ $\theta$ $\le$ 360°and express answer in degrees to two decimal places.

A) 162.75^o
B) 197.25^o
C) 81.38^o
D) no solution

Question 43

Solve the given trigonometric equation on0° $\le$ $\theta$ $\le$ 360° and express answer in degrees to two decimal places.

A) 42.51^o, 222.51^o
B) 42.51^o, 137.49^o
C) 222.51^o, 317.49^o
D) 137.49^o, 317.49^o

Question 44

Solve the given trigonometric equation on 0° $\le$ $\theta$ $\le$ 360°and express answer in degrees to two decimal places.

A) 80.41^o, 279.59^o
B) 80.41^o, 99.59^o
C) 279.59^o, 260.41^o
D) 99.59^o, 260.41^o

Question 45

Solve the given trigonometric equation on 0° $\le$ $\theta$ $\le$ 360° and express answer in degrees to two decimal places.

A) 25.66^o, 334.34^o
B) 334.34^o, 205.66^o
C) 25.66^o, 154.34^o
D) 154.34^o, 205.66^o

Question 46

Solve the given trigonometric equation on 0° $\le$ $\theta$ $\le$ 360° and express answer in degrees to two decimal places.

A) 210.00°, 330.00°, 30.00°, 150.00°
B) 210.00°, 30.00°, 30.00°, 210.00°
C) 330.00°, 30.00°, 150.00°, 330.00°
D) 30.00°, 150.00°, 210.00°, 330.00°

Question 47

Solve the given trigonometric equation on 0° $\le$ $\theta$ $\le$ 360°and express answer in degrees to two decimal places.

A) 116.57°, 296.57°, 26.57°, 206.57°
B) 116.57°, 63.43°, 26.57°, 153.43°
C) 296.57°, 243.43°, 206.57°, 333.43°
D) 63.43°, 243.43°, 153.43°, 333.43°

Question 48

The monthly sales of soccer balls is approximated by
where x is the number of the month (January is x = 1, etc.) During which two months do the sales reach 2346.4?

A) February and April
B) February and May
C) January and April
D) February and March

Question 49

Deer Population. The number of deer on an island is given by

, where x is the number of years since 2000. Which is the first year after 2000 that the number of deer reaches 160.

Question 50

Solve the given trigonometric equation exactly on the interval, 0 ≤ x ≤ 2π.

Question 51

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 52

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 53

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 54

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 55

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 56

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 57

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 58

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 59

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 60

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 61

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 62

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 63

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 64

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 65

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 66

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Question 67

Solve the trigonometric equation on 0° ≤ x ≤ 360°. Give answers in degrees and round to two decimal places.

Question 68

Solve the trigonometric equation on 0° ≤ x ≤ 360°. Give answers in degrees and round to two decimal places.

Question 69

Solve the trigonometric equation on 0° ≤ x ≤ 360°. Give answers in degrees and round to two decimal places.

Question 70

If a person breathes in and out every 3 seconds, the volume of air in their lungs can be modeled by

, where A is in liters of air and x is in seconds. How many seconds into the cycle is the volume of air equal to 2.00 liters?

Question 71

The figure below shows the graph of

between -2π and 2π. The maximum and minimum values of the curve occur at the turning points and are found in the solutions of the equation

. Solve for the coordinates of the turning points of the curve between

Question 72

The figure below shows the graph of

between -2π and 2π. The maximum and minimum values of the curve occur at the turning points and are found in the solutions of the equation

. Solve for the coordinates of the turning points of the curve between

Question 73

Solve the given trigonometric equation exactly over the interval, 0 $\le$ x $\le$ 2 $\pi$ .

A) 0
B) 0, $\pi$
C) 0, $\pi$ /2, $\pi$
D) no solution

Question 74

Solve the given trigonometric equation exactly over the interval, 0 $\le$ x $\le$ 2 $\pi$ .

A) $\pi$ /2
B) $\pi$ /2, 3 $\pi$ /2
C) $\pi$ /2, $\pi$ , 3 $\pi$ /2
D) no solution

Question 75

Solve the given trigonometric equation exactly over the interval, 0 $\le$ x $\le$ 2 $\pi$ .

A) $\pi$ , $\pi$ /2
B) 0, $\pi$ , $\pi$ /2
C) 0, 2 $\pi$ , $\pi$ /2, 3 $\pi$ /2
D) 0, $\pi$ , 2 $\pi$ , $\pi$ /2, 3 $\pi$ /2

Question 76

Solve the given trigonometric equation exactly over the interval, 0 $\le$ x $\le$ 2 $\pi$ .

A)
B)
C)
D)

Question 77

Solve the given trigonometric equation exactly over the interval, 0 $\le$ x $\le$ 2 $\pi$ .

A)
B)
C)
D)

Question 78

Solve the given trigonometric equation exactly over the interval, 0 $\le$ x $\le$ 2 $\pi$ .

A)
B)
C)
D)

Question 79

Solve the given trigonometric equation exactly over the interval, 0 $\le$ x $\le$ 2 $\pi$ .

A)
B)
C)
D)

Question 80

Solve the given trigonometric equation exactly over the interval, 0 $\le$ x $\le$ 2 $\pi$ .

A)
B)
C)
D)