Question 1

Evaluate the expression exactly if possible. If not possible, state why.

Accepted Answer

The answer of Evaluate the expression exactly if possible. If...

Question 2

Evaluate the expression exactly if possible. If not possible, state why.

Accepted Answer

The answer of Evaluate the expression exactly if possible. If...

Question 3

Evaluate the expression exactly.

Accepted Answer

The answer of Evaluate the expression exactly. 
...

Question 4

Evaluate the expression exactly.

Accepted Answer

The answer of Evaluate the expression exactly. 
...

Question 5

The number of hours of daylight in San Diego, California, can be modeled with
H(t) =12 + 2.4sin(0.017t - 1.377) where t is the day of the year (January 1, t = 1 etc) For what values of t is the number of hours equal to 14? Round to 2 decimal places.

Accepted Answer

The number of hours of daylight is equal to 14 when H(t) = 14. Solving this equation gives t = 138.95 and t = 315.45.

Question 6

The horizontal movement of a point that is k kilometers away from an earthquake's fault line can be estimated with

Where M is the movement of the point in meters, f is the total horizontal displacement occurring along the fault line, k is the distance of the point from the fault line, and d is the depth in kilometers of the focal point of the earthquake. If an earthquake produced a displacement, f, of 2.8 meters and the depth of the focal point was 1.2 kilometers, then what is the movement, M , of a point that is 11.3 kilometers from the fault line? Round to 2 decimal places.

Accepted Answer

The answer of The horizontal movement of a point that...

Question 7

A museum patron whose eye level is 4 feet above the floor is studying a painting that is 8 feet in height and mounted on the wall 4 feet above the floor. If the patron is x feet from the wall, $\theta$ is the angle that the patron's eye sweeps from the top to the bottom of the painting. Find the measure of the angle $\theta$ for x = 20. Round to the nearest degree).

Accepted Answer

The angle can be found using trigonometry, specifically the tangent function, which relates an angle of a right triangle to the ratio of the opposite side over the adjacent side. Here, the opposite sides are the distances from the eye level to the top and bottom of the painting (4 feet to the top and 12 feet to the bottom), and the adjacent side is the distance from the wall (20 feet). Calculating the angles to the top and bottom of the painting and subtracting gives the total angle swept by the eye. The calculations yield an angle of approximately 22 degrees.

Question 8

Write the expression in terms of x.
If

Accepted Answer

The answer of Write the expression in terms of x.
If
...

Question 9

Write cos x sin 6x as a sum or difference of sines and/or cosines.

Accepted Answer

The answer of Write cos x sin 6x as a...

Question 10

Write

As a sum or difference of sines and/or cosines.

Accepted Answer

The answer of Write

As a sum or difference of sines...

Question 11

Write cos 2 x cos 8 x as a sum or difference of sines and/or cosines.

Accepted Answer

The answer of Write cos 2 x cos 8 x...

Question 12

Write

As a product of sines and/or cosines.

Accepted Answer

The answer of Write

As a product of sines and/or cosines.
...

Question 13

Write sin 8x sin 5x as a sum or difference of sines and/or cosines.

Accepted Answer

The answer of Write sin 8x sin 5x as a...

Question 14

Write

As a product of sines and/or cosines.

Accepted Answer

The answer of Write

As a product of sines and/or cosines.
...

Question 15

Write sin 3x cos 8x as a sum or difference of sines and/or cosines.

Accepted Answer

The answer of Write sin 3x cos 8x as a...

Question 16

Write

As a product of sines and/or cosines.

Accepted Answer

The answer of Write

As a product of sines and/or cosines.
...

Question 17

Write cos 10x - cos 4x as a product of sines and/or cosines.

Accepted Answer

The answer of Write cos 10x - cos 4x as...

Question 18

Write sin 4x - sin 2x as a product of sines and/or cosines.

Accepted Answer

The answer of Write sin 4x - sin 2x as...

Question 19

Write sin 10x + sin 2 x as a product of sines and/or cosines.

Accepted Answer

The answer of Write sin 10x + sin 2 x...

Question 20

Write sin1.2x + sin0.4x as a product of sines and/or cosines.

Accepted Answer

The answer of Write sin1.2x + sin0.4x as a product...

Quiz 6: Analytic Trigonometry

Evaluate the expression exactly if possible. If not possible, state why.

Evaluate the expression exactly if possible. If not possible, state why.

Evaluate the expression exactly.

Evaluate the expression exactly.

The number of hours of daylight in San Diego, California, can be modeled with H(t) =12 + 2.4sin(0.017t - 1.377) where t is the day of the year (January 1, t = 1 etc) For what values of t is the number of hours equal to 14? Round to 2 decimal places.

Write the expression in terms of x. If

Write cos x sin 6x as a sum or difference of sines and/or cosines.

Write As a sum or difference of sines and/or cosines.

Write cos 2 x cos 8 x as a sum or difference of sines and/or cosines.

Write As a product of sines and/or cosines.

Write sin 8x sin 5x as a sum or difference of sines and/or cosines.

Write As a product of sines and/or cosines.

Write sin 3x cos 8x as a sum or difference of sines and/or cosines.

Write As a product of sines and/or cosines.

Write cos 10x - cos 4x as a product of sines and/or cosines.

Write sin 4x - sin 2x as a product of sines and/or cosines.

Write sin 10x + sin 2 x as a product of sines and/or cosines.

Write sin1.2x + sin0.4x as a product of sines and/or cosines.