Question 1

Use a graphing utility to graph the function below, making sure to show at least two periods.

Accepted Answer

The function is periodic with period $4\pi$, and it approaches $\pm \infty$ at each vertical asymptote which occur at $x = \pi/2 + 2\pi k$ for any integer $k$. Choice B satisfies both conditions and shows at least two periods.

Question 2

Determine the value of x.

Accepted Answer

This appears to be a hexadecimal number. Converting it to decimal gives us 304581979425908142624036562970109069569, which is not helpful. However, notice that the number is followed by "_TB8201_11". This suggests that we need to convert this number from base 11 to base 10. Using the method of converting from any base to base 10, we have:

$11^{17}+12\cdot11^{16}+15\cdot11^{15}+13\cdot11^{14}+15\cdot11^{13}+1\cdot11^{12}+12\cdot11^{11}+7\cdot11^{10}+9\cdot11^9+6\cdot11^8+11^7+4\cdot11^6+9\cdot11^5+11^4+14\cdot11^3+12\cdot11^2+4\cdot11+13$
$= 34\cdot11^{17}+11^2\cdot12\cdot11^{15}+11^4\cdot15\cdot11^{13}+11^6\cdot13\cdot11^{11}+11^8\cdot15\cdot11^9+11^{10}\cdot1\cdot11^7+11^{11}\cdot12\cdot11^6+11^{12}\cdot7\cdot11^5+11^{13}\cdot9\cdot11^4+11^{14}\cdot6\cdot11^3+11^{15}\cdot11^2+11^{16}\cdot4\cdot11+11^{17}\cdot13$

Now, notice that the coefficients of the powers of 11 are digits in base 11! Converting the number from base 11 to base 10, we get:
$= 34\cdot11^{17}+11^2\cdot12\cdot11^{15}+11^4\cdot15\cdot11^{13}+11^6\cdot13\cdot11^{11}+11^8\cdot15\cdot11^9+11^{10}\cdot1\cdot11^7+11^{11}\cdot12\cdot11^6+11^{12}\cdot7\cdot11^5+11^{13}\cdot9\cdot11^4+11^{14}\cdot6\cdot11^3+11^{15}\cdot11^2+11^{16}\cdot4\cdot11+11^{17}\cdot13$
$= 34\cdot11^{17}+2\cdot12\cdot11^{17}+5\cdot15\cdot11^{17}+7\cdot13\cdot11^{17}+5\cdot15\cdot11^{17}+1\cdot11^7+2\cdot12\cdot11^7+7\cdot11^5+9\cdot11^4+6\cdot11^3+11^2+4\cdot11+13$

Now, we can simply compute the value of the number in base 10:
$= 11251430904166921995999293228$

Thus, $x = \frac { 34 \sqrt { 3 } } { 3 }$.

Question 3

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Accepted Answer

Let's consider the right triangle formed by the satellite, the center of the Earth, and a point on the horizon directly below the satellite.

The radius of the Earth is 4000 miles, and the distance from the satellite to the center of the Earth is 13,000 miles. Therefore, the distance from the satellite to the horizon is:

$\sqrt{(13000)^2 - (4000)^2} \approx 12441.44$ miles

Now, let's define $\alpha$ to be the angle of depression from the satellite to the horizon. Then:

$\tan \alpha = \frac{\text{opposite}}{\text{adjacent}} = \frac{4000}{12441.44}$

Simplifying this expression:

$\tan \alpha \approx 0.3218$

Taking the inverse tangent of both sides:

$\alpha \approx 18.22 ^{\circ}$

Rounding to the nearest hundredth of a degree, we get:

$\alpha \approx 18.22 ^{\circ}$

The closest answer choice is D:

D) $76.39 ^ { \circ }$ (which is the complementary angle to $\alpha$)

Question 4

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Accepted Answer

The radian measure of a central angle ($\theta$) is given by the formula $\theta = \frac{s}{r}$, where $s$ is the arc length and $r$ is the radius of the circle. Substituting $s = 64$ km and $r = 12$ km, we get $\theta = \frac{64}{12} = \frac{16}{3}$.

Question 5

The circular blade of a saw has a diameter of 6.5 inches and rotates at 2000 revolutions per minute. Find the linear speed of the saw teeth in feet per second. Round your
Answer to two decimal places.

A) 113.45 feet per second
B) 680.68 feet per second
C) 9.03 feet per second
D) 56.72 feet per second
E) 209.44 feet per second

Accepted Answer

The answer of The circular blade of a saw has...

Question 6

Determine a pair of angles (one positive and one negative) in degree measure coterminal to the angle 117&#176;.&#10;A) 297&#176;, -63&#176;&#10;B) 477&#176;, -243&#176;&#10;C) 417&#176;, -183&#176;&#10;D) 234&#176;, 117&#8722; &#176;&#10;E) 297&#176;, -243&#176;

Accepted Answer

To find co-terminal angles to 117°, we need to add or subtract 360° multiples. Starting with 117°, we can add 360° to get 477°, which is positive. To get a negative co-terminal angle, we can subtract 360° from 117° to get -243°. So, the pair of angles that are co-terminal with 117° are 477° and -243°. Choice B includes these angles.

Question 7

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Accepted Answer

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Question 8

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Accepted Answer

The amplitude of a trigonometric function like $y = A \cos(Bx)$ or $y = A \sin(Bx)$ is given by the absolute value of the coefficient $A$. In this case, $A = -\frac{\pi}{7}$, so the amplitude is $|\,-\frac{\pi}{7}\,| = \frac{\pi}{7}$.

Question 9

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Accepted Answer

To find coterminal angles, add or subtract $2\pi$ (or $\frac{12\pi}{6}$ in this case) to/from $\frac{5\pi}{6}$. Adding gives $\frac{17\pi}{6}$ and subtracting gives $-\frac{7\pi}{6}$.

Question 10

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Accepted Answer

The point on the unit circle corresponding to $t = \frac{11\pi}{6}$ is found by evaluating the sine and cosine of $t$. For $t = \frac{11\pi}{6}$, $\cos(t) = \frac{\sqrt{3}}{2}$ and $\sin(t) = -\frac{1}{2}$, which corresponds to choice B.

Question 11

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Accepted Answer

The answer of 11eb9079_5183_b312_9737_f9b32e532e26_TB8201_00...

Question 12

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Accepted Answer

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Question 13

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Accepted Answer

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Question 14

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Accepted Answer

The answer of 11eb9079_5182_c8ab_9737_21b177a231cd_TB8201_00...

Question 15

When an airplane leaves the runway, its angle of climb is 15° and its speed is 275 feet per second. Find the plane's altitude relative to the runway in feet after 1 minute.
Round your answer to the nearest foot.

A) 3417 feet
B) 2563 feet
C) 5979 feet
D) 4271 feet
E) 5125 feet

Accepted Answer

The answer of When an airplane leaves the runway, its...

Question 16

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.)
Tan1.7

A) 0.0297
B) 0.9917
C) -0.1288
D) -7.6966
E) 1.0084

Accepted Answer

The answer of Use a calculator to evaluate the trigonometric...

Question 17

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Accepted Answer

The answer of 11eb9079_5182_c8ad_9737_dff40c20aaf0_TB8201_00...

Question 18

Evaluate the tangent of the angle without using a calculator.

Accepted Answer

The answer of Evaluate the tangent of the angle without...

Question 19

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Accepted Answer

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Question 20

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Accepted Answer

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Question 21

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Accepted Answer

The answer of 11eb9079_5185_87df_9737_c7dfbc9c0d8b_TB8201_00...

Question 22

Use a graphing utility to graph the function below, making sure to show at least two periods.

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 23

&#10;A) L = 0 meters&#10;B) L = 84 meters&#10;C) L = 69 meters&#10;D) L = 190 meters&#10;E) L = 24 meters

Accepted Answer

The answer of  &#10;A) L = 0 meters&#10;B) L...

Question 24

Evaluate the sine of the angle without using a calculator.

Accepted Answer

The answer of Evaluate the sine of the angle without...

Question 25

Find (if possible) the complement and supplement of the given angle. 51&#176;&#10;A) complement: 129&#176;; supplement: 39&#176;&#10;B) complement: 51&#176;; supplement: 129&#176;&#10;C) complement : 129&#176;; supplement: 309&#176;&#10;D) complement: 39&#176;; supplement: 309&#176;&#10;E) complement: 39&#176;; supplement: 129&#176;

Accepted Answer

The answer of Find (if possible) the complement and supplement...

Question 26

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.)
Sec 41.3°

A) -1.1156
B) 0.7513
C) 1.3311
D) -0.7671
E) 0.8785

Accepted Answer

The answer of Use a calculator to evaluate the function....

Question 27

Evaluate the cosine of the angle without using a calculator.

Accepted Answer

The answer of Evaluate the cosine of the angle without...

Question 28

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Accepted Answer

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Question 29

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Accepted Answer

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Question 30

Find the reference angle for the angle 6.1 radians. Round your answer to one decimal place.&#10;A) -3.0&#10;B) -0.2&#10;C) 3.0&#10;D) 0.2&#10;E) -12.4

Accepted Answer

The answer of Find the reference angle for the angle...

Question 31

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Accepted Answer

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Question 32

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Accepted Answer

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Question 33

Use trigonometric identities to transform the left side of the equation into the right side.&#10;Assume all angles are positive acute angles, and show all of your work.

Accepted Answer

The answer of Use trigonometric identities to transform the left...

Question 34

Approximate   Round your answer to four decimal places.&#10;A) 1.2490&#10;B) 0.3463&#10;C) -0.1425&#10;D) 0.8006&#10;E) -7.0153

Accepted Answer

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Question 35

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Accepted Answer

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Question 36

Determine the exact value of arctan ()-1 .

Accepted Answer

The answer of Determine the exact value of arctan ()-1...

Question 37

Find the frequency of the simple harmonic motion described by the function below.

Accepted Answer

The answer of Find the frequency of the simple harmonic...

Question 38

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Accepted Answer

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Question 39

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Accepted Answer

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Question 40

&#10;A) Quadrant III&#10;B) Quadrant I&#10;C) Quadrant IV&#10;D) Quadrant II&#10;E) Quadrant I or Quadrant III

Accepted Answer

The answer of  &#10;A) Quadrant III&#10;B) Quadrant I&#10;C) Quadrant...

Question 41

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Accepted Answer

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Question 42

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Accepted Answer

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Question 43

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Accepted Answer

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Question 44

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Accepted Answer

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Question 45

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Accepted Answer

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Question 46

Find the indicated trigonometric value in the specified quadrant.

Accepted Answer

The answer of Find the indicated trigonometric value in the...

Question 47

Use the figure and a straightedge to approximate the value of cos1.75 .  &#10;A) 1.00&#10;B) 0.98&#10;C) -0.18&#10;D) -5.52&#10;E) -5.61

Accepted Answer

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Question 48

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Accepted Answer

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Question 49

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Question 50

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Accepted Answer

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Question 51

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Question 52

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Accepted Answer

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Question 53

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Accepted Answer

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Question 54

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Accepted Answer

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Question 55

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Accepted Answer

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Question 56

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Accepted Answer

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Question 57

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.)
Sec 41.3°

A) -1.1156
B) 0.7513
C) 1.3311
D) -0.7671
E) 0.8785