Honors Pre-Calculus > Module 04: Trigonometric Functions > Flashcards

Module 04: Trigonometric Functions Flashcards

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1
Q

Convert the angle 13°38’35” to decimal degrees, and round to the nearest hundredth of a degree. (2 points)

  1. 13.70°
  2. 13.65°
  3. 13.60°
  4. 13.64°
A

4. 13.64°

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2
Q

Convert 17.47° to degrees, minutes, and seconds. (2 points)

  1. 17°28’18”
  2. 17°28’0”
  3. 17°28’12”
  4. 17°28’47”
A

3. 17°28’12”

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3
Q

Convert 36° from degrees to radians.

A

π/5

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4
Q

Convert the radian measure to degree measure. Use the value of π found on a calculator, and round answers to two decimal places. (2 points)

9π/12

  1. 135°
  2. 160°
  3. 270°
  4. 240π
A

1. 135°

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5
Q

Use the arc length formula and the given information to find s. Show your work for full credit. (2 points)

r = 20 ft θ¸ = 19° s = ?

A

Θ = 19°

Θ = 19° * π/180

Θ = 19π/180

s=rΘ

s=(20ft)(19π180)

s=380π180

s=19π9

s=2.11π

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6
Q

Find the exact values of sin A and cos A. Write fractions in lowest terms. (2 points)

  1. sin A = 4/3; cos A = 3/4
  2. sin A = 5/4 ; cos A = 5/3
  3. sin A = 3/5 ; cos A = 4/5
  4. sin A = 4/5 ; cos A = 3/5
A

4. sin A = 4/5 ; cos A = 3/5

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7
Q

An acute angle θ is in a right triangle with sin θ = 2/3. What is the value of cot θ? (3 points)

A

√5/2

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8
Q

An acute angle θ is in a right triangle with cos θ = 9/10. What is the value of sec θ? (2 points)

A

10/9

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9
Q

Solve for x. Round your answer to two decimal places. Show your work for full credit. (3 points)

A

sinΘ=opp/hyp

sin(30­°)=10x

x=10sin(30°)

x=100.5

x=20

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10
Q

Is the function cot t positive or negative in Quadrant II? (3 points)

Positive

Negative

A

Negative

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11
Q

Find the measures of two angles, one positive and one negative, that are coterminal with π/5 . (2 points)

A

11π/5; -9π/5

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12
Q

Evaluate sin 60° without using a calculator by using ratios in a reference triangle. (3 points)

A
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13
Q

Determine the sign of sin 5π/4 without using a calculator. (2 points)

  1. Negative
  2. Positive
A

Negative

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14
Q

Find the value of cos θ for the angle shown. (2 points)

  1. cos θ = 7/4
  2. cos θ = √33/4
  3. cos θ = 4/7
  4. cos θ = √33/7
A

cos θ = 4/7

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15
Q
A
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16
Q

The point P(21, 28) is on the terminal side of θ. Evaluate sin θ. (3 points)

  1. 3/4
  2. 4/5
  3. 3/5
  4. 4/3
A

2. 4/5

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17
Q

Choose the point on the terminal side of -45°. (2 points)

  1. (-3, -3)
  2. (4, -4)
  3. (5, 5)
  4. (-2, 2)
A

2. (4, -4)

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18
Q

Find the point on the terminal side of θ = -3π/4 that has an x coordinate of -1. Show your work for full credit. (3 points)

A
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19
Q

Find the amplitude of y = -2 sin x. (2 points)

A

2

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20
Q

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).
f(x) = 4 cos x ; g(x) = cos x

  1. Vertical stretch by a factor of 4
  2. Horizontal stretch by a factor of 4
  3. Vertical shrink by a factor of 1/4
  4. Horizontal shrink by a factor of 1/4
A

1. Vertical stretch by a factor of 4

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21
Q

Identify the maximum and minimum values of the function y = 8 cos x in the interval [-2π , 2π]. Use your understanding of transformations, not your graphing calculator. (3 points)

22
Q

Analyze the function f(x) = sec 2x.

Include:

  • Domain and range
  • Period and Amplitude
  • Two Vertical Asymptotes (6 points)
23
Q

From a boat on the lake, the angle of elevation to the top of a cliff is 26°1’. If the base of the cliff is 205 feet from the boat, how high is the cliff (to the nearest foot)? (2 points)

  1. 113 ft
  2. 110 ft
  3. 103 ft
  4. 100 ft
24
Q

From a balloon 760 feet high, the angle of depression to the ranger headquarters is 89°18’. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)? (3 points)

25
Bob is driving along a straight and level road toward a mountain. At some point on his trip, he measures the angle of elevation to the top of the mountain and finds it to be 23°29'. Find the height of the mountain to the nearest foot if Bob is 16,194.6 feet from the center of the mountain at the base. (2 points) 1. 7036 ft 2. 7136 ft 3. 70,357 ft 4. 703,574 ft
**1.** 7036 ft
26
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 16°18'. When the boat stops, the angle of depression is 48°51'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place. (3 points)
27
Convert the angle 35°58'38" to decimal degrees, and round to the nearest hundredth of a degree. (1 point)
35.98°
28
Convert 210° from degrees to radians. Use the value of π found on a calculator, and round answers to four decimal places, as needed. (1 point)
7π/6
29
Use the arc length formula and the given information to find r. s = 16 cm, θ= 48°; r = ? (1 point)
r = 60/π cm
30
An acute angle θ is in a right triangle with sin θ= 6/7 . What is the value of cot θ? (1 point)
√13/6
31
Solve for x. Round your answer to 2 decimal places. (1 point) 1. 3.71 2. 13.21 3. 5.94 4. 8.25
**2.** 13.21
32
Find the measures of two angles, one positive and one negative, that are coterminal with π/2 .
5π/2; -3π/2
33
Find the amplitude y = 5 sin 1/2x. (1 point)
5
34
Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). **f(x) = cos ; g(x) = cos x** 1. Horizontal stretch by a factor of 2 2. Vertical stretch by a factor of 2 3. Vertical shrink by a factor of 1/2 4. Horizontal shrink by a factor of 1/2
**2.** Vertical stretch by a factor of 2
35
Find the exact value of cos-1 (√3/2)
π/6
36
Use a calculator to find the approximate value of cos-1(0.45). (1 point) 1. 53.49° 2. 63.26° 3. 26.74° 4. 24.23°
**2.** 63.26°
37
Find the exact real value of arcsin (√3/2)
π/3
38
Find the exact value of cos (arcsin (5/13)).
12/13
39
From a boat on the lake, the angle of elevation to the top of a cliff is 14°28'. If the base of the cliff is 743 feet from the boat, how high is the cliff (to the nearest foot)? (1 point) 1. 195 ft 2. 192 ft 3. 205 ft 4. 202 ft
**2.** 192 ft
40
What are the trigonometric functions forms?
Sine: y = a \* sin (bx + c) + d Cosine: y = a \* cos (bx + c) + d Tangent: y = a \* tan (bx + c) + d a is the **amplitude** (only for sin and cos) Sine, Cosine, Secant and Cosecant all have a period of 2pi/b Tangent and Cotangent have periods of pi/b b helps us find the **period** from the equation period=2pi/b Only tangent, cotangent, secant, and cosecant have asymptotes, and again, it depends which function we are working with as to what we need to do. c is the **phase shift** (This is a horizontal shift of the curve) d is the **vertical shift**
41
42
43
What is the amplitude (a)?
* a* → amplitude of the curve * determines verticle stretching or shrinking * range: -a ≤ y ≤ a l a l → amplitude
44
What is the period (b)?
* b →* period of graph * determines horizontal stretching or shrinking **2π/b** *_Positive b_* * value \< 1 stretches period beyond 2π * value \> 1 shrinks period less than 2π *_Negative b_* * sin(-x) = -sin(x) * cos(-x) = cos(x).
45
What is the Phase Shift (c)?
* c →* phase shift (horizontal) along x-axis * distance: c /d (*phase shift)*
46
What is the endpoint on a graph?
1. bx - c = 0 2. bx - c = 2π
47
What is the inverse sine function?
48
What is the inverse cosine?
49
What is inverse tangent?
50
What is the angle of elevation and depression?
tangent-value = height-of-building ÷ distance-from-building **Angle of Elevation**: Angle through which the eye moves up from horizontal to look at something above **Angle of Depression**: Angle through which the eye moves up from horizontal to look at something above
51
Honors Pre-Calculus
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