Question 1

Find the value of cos 324.7° rounded to four significant digits.
A) 0.8161
B) 1.2161
C) -0.5441
D) 0.5441
E) -0.8161

Accepted Answer

To find the value of cos 324.7°, we can use a calculator or trigonometric tables. The cosine of an angle in standard position is the same as the cosine of its reference angle in the first quadrant. The reference angle for 324.7° is 360° - 324.7° = 35.3°. The cosine of 35.3° is positive in the fourth quadrant, and its value is approximately 0.8161 when rounded to four significant digits.

Question 2

Find the value of cos 304° rounded to four significant digits.
A) 0.2796
B) 0.7592
C) 0.5592
D) -1.0000
E) 0.1796

Accepted Answer

C

Question 3

Graph the equation for values of x between 0° and 360° in multiples of 30°. y = 5 sin x
A) 
B) 
C) 
D) 
E)

Accepted Answer

D

Question 4

Find the value of tan 402.1° rounded to four significant digits.
A) -1.3554
B) 0.8036
C) 1.3554
D) 0.9036
E) -0.9036

Accepted Answer

The answer of Find the value of tan 402.1° rounded...

Question 5

The maximum voltage in a simple generator is V. The changing voltage v as the coil rotates is given by v = V sin x. Graph this equation in multiples of 30° for one complete revolution of the coil for the given value of V. V = 42 Volts
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The maximum voltage in a simple generator...

Question 6

Find the value of sin 158.8° rounded to four significant digits.
A) 0.3616
B) 0.5616
C) 0.1808
D) -0.3616
E) -0.1808

Accepted Answer

To find the value of sin 158.8°, we can use a calculator or trigonometric tables. Since 158.8° is in the second quadrant, where sine values are positive, we expect a positive result. The exact value might not be readily available without calculation, but using a scientific calculator or trigonometric function, sin(158.8°) ≈ 0.3616.

Question 7

Find the value of tan 174.6° rounded to four significant digits.
A) 0.2055
B) 0.0945
C) -0.0473
D) -0.0945
E) 0.0473

Accepted Answer

The tangent of an angle in the third quadrant (where 174.6° lies) is negative, and since tan(θ) = tan(θ + n*180°) for any integer n, tan(174.6°) = tan(174.6° - 180°) = tan(-5.4°). The value of tan(-5.4°) is negative and close to -0.0945 when rounded to four significant digits.

Question 8

Graph the equation for values of x between 0° and 360° in multiples of 10°. y = 5 cos 2x
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Graph the equation for values of x...

Question 9

Find the value of tan 243.6° rounded to four significant digits.
A) 2.014
B) -3.357
C) 3.357
D) -2.014
E) 1.614

Accepted Answer

The answer of Find the value of tan 243.6° rounded...

Question 10

Find the value of sin 320° rounded to four significant digits.
A) -0.3214
B) -0.4428
C) 0
D) -0.6428
E) -0.4214

Accepted Answer

Using the fact that the sine function has a period of 360°, we can subtract 360° from 320° until we obtain an angle between 0° and 360°.

320° - 360° = -40°
-40° + 360° = 320°

We can see that sin 320° is negative, since it corresponds to a reference angle in the fourth quadrant, where sine is negative.

To find the value of sin 320°, we can use the sine function of the reference angle 40°:

sin 40° ≈ 0.6428

Since sin 320° is negative, we have:

sin 320° ≈ -0.6428

Rounding to four significant digits, we get:

sin 320° ≈ -0.6428

Therefore, the best choice is D, -0.6428.

Question 11

Find the value of tan 125.1° rounded to four significant digits.
A) -1.223
B) 1.423
C) -0.711
D) -1.423
E) 0.711

Accepted Answer

The value of tan 125.1° can be found using a calculator or trigonometric tables. Since 125.1° is in the second quadrant, where tan is negative, the correct answer is -1.423 when rounded to four significant digits.

Question 12

A radar unit operates at a wavelength of 4.2 cm. Radar waves travel at the speed of light, which is $3.0 \times 10 ^ { 8 }$ . What is the frequency of the radar waves?
A) 7.1 $\times 10 ^ { 6 }$ Hz
B) 7.1 $\times 10 ^ { 9 }$ Hz
C) 6.7 $\times 10 ^ { 9 }$ MHz
D) 7.1 $\times 10 ^ { 9 }$ MHz
E) 6.7 $\times 10 ^ { 9 }$ Hz

Accepted Answer

The answer of A radar unit operates at a wavelength...

Question 13

Find the value of sin 301.8° rounded to four significant digits.
A) -1.1199
B) -0.4449
C) -1.1749
D) 0
E) -0.8499

Accepted Answer

To find the value of sin(301.8°), we first need to convert it to an angle between 0° and 360°, since sine is a periodic function with a period of 360°.

301.8° is greater than 360°, so we can subtract 360° from it to get an equivalent angle between 0° and 360°:

301.8° - 360° = -58.2°

Since sine is negative in the third and fourth quadrants of the unit circle (where the x-coordinate is negative), we can find that the sine of -58.2° is equal to the sine of 121.8°:

sin(-58.2°) = sin(121.8°)

To find the sine of 121.8°, we can use the fact that the sine function has a period of 360° and is symmetric about the line x = 180°:

sin(121.8°) = sin(121.8° - 360°) = sin(-238.2°)

Since -238.2° is equivalent to 121.8° in terms of the sine function, we can use the sine of 121.8° to approximate the sine of -58.2° and therefore the sine of 301.8°:

sin 301.8° = sin(121.8°) ≈ -0.8499 (rounded to four significant digits)

Therefore, the best choice is E.

Question 14

Graph the equation for values of x between 0° and 360° in multiples of 10°. y = 2 sin 4x
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Graph the equation for values of x...

Question 15

Find the value of cos 315° rounded to four significant digits.
A) 0.7071
B) 0.2536
C) 0.4071
D) -0.5000
E) 0.3536

Accepted Answer

Cos 315° is equivalent to cos(360° - 45°), which simplifies to cos 45°. The exact value of cos 45° is √2/2, which is approximately 0.7071 when rounded to four significant digits.

Question 16

Find the value of sin 140° rounded to four significant digits.
A) 0.6428
B) -1.0000
C) 0.2214
D) 0.3214
E) 0.2428

Accepted Answer

The value of sin 140° can be found using the unit circle or a calculator. Since 140° is in the second quadrant, where sine values are positive, the correct answer is A) 0.6428, rounded to four significant digits.

Question 17

Find the value of cos 170.5° rounded to four significant digits.
A) 0.5000
B) 0.9863
C) -0.9863
D) -0.4931
E) -0.8863

Accepted Answer

Use the identity cos(x) = cos(360° - x) to write 
cos 170.5° = cos(360° - 170.5°) = cos 189.5°.
Then, use the fact that cos(x) = -cos(x - 180°) to write 
cos 189.5° = -cos(9.5°).
Finally, use the fact that cos(10°) ≈ 0.9848 (which can be found on a unit circle or calculated using a calculator) to estimate 
cos 9.5° ≈ cos 10° ≈ 0.9848.
Since we have a negative sign, the value of cos 170.5° rounded to four significant digits is approximately -0.9863, which corresponds to choice C.

Question 18

Find the period of the wave whose frequency is 6.2 MHz.
A) 0.15 s
B) 0.16 ms
C) 0.15 ms
D) 0.16 μs
E) 0.15 μs

Accepted Answer

The answer of Find the period of the wave whose...

Question 19

Find the period of the wave whose frequency is 4.8 kHz.
A) 0.26 μs
B) 0.21 ms
C) 0.26 ms
D) 0.26 s
E) 0.21 s

Accepted Answer

The answer of Find the period of the wave whose...

Question 20

Graph the equation for values of x between 0° and 360° in multiples of 30°. y = 5 cos x
A) 
B) 
C) 
D) 
E)

Accepted Answer

The graph of y = 5 cos x is a cosine curve with an amplitude of 5 and a period of 360°. The value of the cosine function varies between -5 and 5.

For x = 0°, y = 5 cos 0° = 5. 
For x = 30°, y = 5 cos 30° = 5(√3)/2 ≈ 4.33. 
For x = 60°, y = 5 cos 60° = 5/2 = 2.5. 
For x = 90°, y = 5 cos 90° = 0. 
For x = 120°, y = 5 cos 120° = -5/2 = -2.5. 
For x = 150°, y = 5 cos 150° = -5(√3)/2 ≈ -4.33. 
For x = 180°, y = 5 cos 180° = -5. 
For x = 210°, y = 5 cos 210° = -5(√3)/2 ≈ -4.33. 
For x = 240°, y = 5 cos 240° = -5/2 = -2.5. 
For x = 270°, y = 5 cos 270° = 0. 
For x = 300°, y = 5 cos 300° = 5/2 = 2.5. 
For x = 330°, y = 5 cos 330° = 5(√3)/2 ≈ 4.33. 
For x = 360°, y = 5 cos 360° = 5.

The points on the graph form a cosine curve that starts at (0°, 5), reaches a maximum of (√3)/2 times the amplitude of 5 at (30°, 4.33), goes through a minimum of 0 at (90°, 0), reaches a maximum of (-√3)/2 times the amplitude of 5 at (150°, -4.33), goes through another minimum of 0 at (270°, 0), and ends at (360°, 5).

The graph of y = 5 cos x for values of x between 0° and 360° in multiples of 30° is shown in option C.

Quiz 14: Trigonometry With Any Angle

Find the value of cos 324.7° rounded to four significant digits.

Find the value of cos 304° rounded to four significant digits.

Graph the equation for values of x between 0° and 360° in multiples of 30°. y = 5 sin x

Find the value of tan 402.1° rounded to four significant digits.

The maximum voltage in a simple generator is V. The changing voltage v as the coil rotates is given by v = V sin x. Graph this equation in multiples of 30° for one complete revolution of the coil for the given value of V. V = 42 Volts

Find the value of sin 158.8° rounded to four significant digits.

Find the value of tan 174.6° rounded to four significant digits.

Graph the equation for values of x between 0° and 360° in multiples of 10°. y = 5 cos 2x

Find the value of tan 243.6° rounded to four significant digits.

Find the value of sin 320° rounded to four significant digits.

Find the value of tan 125.1° rounded to four significant digits.

A radar unit operates at a wavelength of 4.2 cm. Radar waves travel at the speed of light, which is 3.0×1083.0 \times 10 ^ { 8 }3.0×108 . What is the frequency of the radar waves?

Find the value of sin 301.8° rounded to four significant digits.

Graph the equation for values of x between 0° and 360° in multiples of 10°. y = 2 sin 4x

Find the value of cos 315° rounded to four significant digits.

Find the value of sin 140° rounded to four significant digits.

Find the value of cos 170.5° rounded to four significant digits.

Find the period of the wave whose frequency is 6.2 MHz.

Find the period of the wave whose frequency is 4.8 kHz.

Graph the equation for values of x between 0° and 360° in multiples of 30°. y = 5 cos x

A radar unit operates at a wavelength of 4.2 cm. Radar waves travel at the speed of light, which is $3.0 \times 10 ^ { 8 }$ . What is the frequency of the radar waves?