Question 1

Evaluate without the aid of calculators or tables. Answer in radians. cos^-¹1

Accepted Answer

The answer of Evaluate without the aid of calculators or...

Question 2

Simplify without using a calculator.

Accepted Answer

The answer of Simplify without using a calculator. ...

Question 3

Evaluate without using a calculator. Answer in radians.

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The answer of Evaluate without using a calculator. Answer in...

Question 4

Verify the identity.

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Question 5

Evaluate without the aid of calculators or tables, keeping the domain and range of the function in mind. Answer in radians.

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Question 6

Use the following to answer questions :
The graph of y = csc(x) is shown below. Draw the horizontal line y = -1.5. 
-State the quadrant of the principal root.

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The answer of Use the following to answer questions :
The...

Question 7

Evaluate. Answer in exact form.

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Question 8

Evaluate without using a calculator. Answer in radians.

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The answer of Evaluate without using a calculator. Answer in...

Question 9

Evaluate. Answer in exact form.

Accepted Answer

The answer of Evaluate. Answer in exact form. ...

Question 10

Evaluate without the aid of calculators or tables. Answer in radians.

Accepted Answer

The answer of Evaluate without the aid of calculators or...

Question 11

Evaluate using a calculator. Answer to the nearest tenth of a degree. sec^-1 5.593

Accepted Answer

The answer of Evaluate using a calculator. Answer to the...

Question 12

Evaluate using a calculator. Answer in radians to the nearest ten-thousandth, in degrees to the nearest tenth.

Accepted Answer

The answer of Evaluate using a calculator. Answer in radians...

Question 13

Evaluate using a calculator, keeping the domain and range of the function in mind. Answer in radians to the nearest ten-thousandth and in degrees to the nearest tenth.

Accepted Answer

The answer of Evaluate using a calculator, keeping the domain...

Question 14

Evaluate without the aid of calculators or tables. Answer in radians.

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Question 15

The range of a projectile is modeled by the function  , where v is the initial velocity and $\theta$ is the angle at which the object is initially propelled. The maximum range is achieved when $\theta$  = 45°. Use exact values to compute how many feet short of maximum the projectile falls if $\theta$  = 67.5° and v = 104 ft/sec.

Accepted Answer

Using the provided function, we can calculate the maximum range by setting the angle to 45 degrees:

R(45) = v^2/g

where g is the acceleration due to gravity, approximately 32.2 ft/s^2. Plugging in v = 104 ft/s, we get:

R(45) = (104 ft/s)^2 / (32.2 ft/s^2) = 338.05 ft

To find how many feet short of the maximum range the projectile falls when launched at 67.5 degrees, we need to calculate the actual range R(67.5) and subtract the maximum range R(45):

R(67.5) = v^2 * sin(2θ) / g

Plugging in v = 104 ft/s and θ = 67.5 degrees, we get:

R(67.5) = (104 ft/s)^2 * sin(2*67.5°) / (32.2 ft/s^2) = 274.40 ft

The difference between the actual range and the maximum range is:

338.05 ft - 274.40 ft = 63.65 ft

So the projectile falls 63.65 feet short of the maximum range. The closest answer choice is (C) 11ea7f29_4ffd_2c5e_9ecd_4d9dd9011c73_TB3307_11 feet.

Question 16

Use the following to answer questions :
The graph of y = csc(x) is shown below. Draw the horizontal line y = -1.5. 
-State the number of roots in [0, 2$\pi$].

Accepted Answer

Looking at the graph, we can see that the horizontal line y = -1.5 intersects the graph of y = csc(x) twice in the interval [0, 2π]. Therefore, there are 2 roots in this interval. The correct choice is C.

Question 17

Evaluate using a calculator, keeping in mind the domain and range of the function. Answer in radians to the nearest ten-thousandth and in degrees to the nearest tenth.

Accepted Answer

The answer of Evaluate using a calculator, keeping in mind...

Question 18

Evaluate without the aid of calculators or tables, keeping the domain and range of the function in mind. Answer in radians.

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The answer of Evaluate without the aid of calculators or...

Question 19

Evaluate. Answer in exact form.

Accepted Answer

The answer of Evaluate. Answer in exact form. 
...

Question 20

Evaluate. Answer in exact form.

Accepted Answer

The answer of Evaluate. Answer in exact form. ...

Quiz 6: Trigonometric Identities, Inverses, and Equations

Evaluate without the aid of calculators or tables. Answer in radians. cos-1 1

Simplify without using a calculator.

Evaluate without using a calculator. Answer in radians.

Verify the identity.

Evaluate without the aid of calculators or tables, keeping the domain and range of the function in mind. Answer in radians.

Use the following to answer questions : The graph of y = csc(x) is shown below. Draw the horizontal line y = -1.5. -State the quadrant of the principal root.

Evaluate. Answer in exact form.

Evaluate without using a calculator. Answer in radians.

Evaluate. Answer in exact form.

Evaluate without the aid of calculators or tables. Answer in radians.

Evaluate using a calculator. Answer to the nearest tenth of a degree. sec-1 5.593

Evaluate using a calculator. Answer in radians to the nearest ten-thousandth, in degrees to the nearest tenth.

Evaluate using a calculator, keeping the domain and range of the function in mind. Answer in radians to the nearest ten-thousandth and in degrees to the nearest tenth.

Evaluate without the aid of calculators or tables. Answer in radians.

Use the following to answer questions : The graph of y = csc(x) is shown below. Draw the horizontal line y = -1.5. -State the number of roots in [0, 2 π\piπ ].

Evaluate using a calculator, keeping in mind the domain and range of the function. Answer in radians to the nearest ten-thousandth and in degrees to the nearest tenth.

Evaluate without the aid of calculators or tables, keeping the domain and range of the function in mind. Answer in radians.

Evaluate. Answer in exact form.

Evaluate. Answer in exact form.

Evaluate without the aid of calculators or tables. Answer in radians. cos^-¹1

Evaluate using a calculator. Answer to the nearest tenth of a degree. sec^-1 5.593