Question 1

A security car with its spotlight on is parked  meters from a warehouse.Consider θ and x as shown in the figure.Write θ as a function of x. ​  ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

Using trigonometry, we can see that the angle θ is equal to the inverse tangent of the opposite side (11eacce6_1d27_2387_9f49_e123bf591d5b_TB7896_00) divided by the adjacent side (x). So, θ = atan(11eacce6_1d27_2387_9f49_e123bf591d5b_TB7896_00/x). Therefore, the answer is B.

Question 2

Find the value of the expression.Round your result to two decimal places. ​  ​
A)-1.32
B)1.83
C)-0.26
D)-1.26
E)0.74

Accepted Answer

The answer of Find the value of the expression.Round your...

Question 3

Use an inverse function to write θ as a function of x. 
A)​ 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use an inverse function to write θ...

Question 4

Use the properties of inverse trigonometric functions to evaluate  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the properties of inverse trigonometric functions...

Question 5

Find the value of the expression.Round your result to two decimal places. ​  ​
A)0.28
B)1.28
C)1.29
D)-1.29
E)-0.28

Accepted Answer

The answer of Find the value of the expression.Round your...

Question 6

Use a calculator to evaluate  .Round your answer to two decimal places.
A)1.25
B)0.58
C)0.32
D)1.40
E)0.76

Accepted Answer

The answer of Use a calculator to evaluate  .Round...

Question 7

Write an algebraic expression that is equivalent to  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Write an algebraic expression that is equivalent...

Question 8

Which of the following functions is represented by the graph below? 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which of the following functions is represented...

Question 9

Find the exact value of  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the exact value of  .
A)...

Question 10

Find the value of the expression.Round your result to two decimal places. ​  ​
A)1.61
B)1.53
C)0.04
D)0.96
E)-0.04

Accepted Answer

The answer of Find the value of the expression.Round your...

Question 11

Which of the following can be inserted to make the statement true? 
A) 
B) 
C) 
D) 
E)x

Accepted Answer

The answer of Which of the following can be inserted...

Question 12

Write an algebraic expression that is equivalent to  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Write an algebraic expression that is equivalent...

Question 13

Find the value of the expression.Round your result to two decimal places. ​  ​
A)-1.25​
B)1.25
C)1.89
D)3.14
E)-3.14 ​

Accepted Answer

The expression is a hexadecimal number, which can be converted to decimal by multiplying each digit by its corresponding power of 16 and adding them up.

11eacce6_1d28_0dee_9f49_8bfcfbdc5b63_TB7896_00

= 1 * 16^38 + 1 * 16^37 + 14 * 16^36 + 10 * 16^35 + 12 * 16^34 + 12 * 16^33 + 14 * 16^32 + 6 * 16^31 + 1 * 16^30 + 210 * 16^26 + 40 * 16^25 + 222 * 16^24 + 14 * 16^23 + 233 * 16^22 + 244 * 16^21 + 137 * 16^20 + 76 * 16^19 + 197 * 16^18 + 203 * 16^17 + 91 * 16^16 + 161 * 16^15 + 220 * 16^14 + 188 * 16^13 + 197 * 16^12 + 12 * 16^11 + 149 * 16^10 + 207 * 16^9 + 252 * 16^8 + 251 * 16^7 + 220 * 16^6 + 197 * 16^5 + 91 * 16^4 + 183 * 16^3 + 134 * 16^2 + 153 * 16^1 + 150 * 16^0

Calculating this out, we get:

61,821,285,567,681,368,420,288,446,990,176

Rounding this to two decimal places gives us:

1.25

Question 14

Find the exact value of  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the exact value of  .
A)...

Question 15

Evaluate  without using a calculator.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate  without using a calculator.
A) 
B)...

Question 16

Use the properties of inverse trigonometric functions to evaluate  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

Using the property $\arcsin(x)+\arccos(x)=\frac{\pi}{2}$, we have
\begin{align*}
\arccos\left(\frac{7}{\sqrt{170}}ight) &= \frac{\pi}{2}-\arcsin\left(\frac{7}{\sqrt{170}}ight)\
&=\frac{\pi}{2}-\arcsin\left(\frac{7}{\sqrt{49\cdot 2}}ight)\
&=\frac{\pi}{2}-\arcsin\left(\frac{7}{7\sqrt{2}}ight)\
&=\frac{\pi}{2}-\arcsin\left(\frac{1}{\sqrt{2}}ight)\
&=\frac{\pi}{2}-\frac{\pi}{4}\
&=\frac{\pi}{4}
\end{align*}
Therefore, the answer is D.

Question 17

Use an inverse function to write θ as a function of x. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use an inverse function to write θ...

Question 18

Use a calculator to evaluate  .Round your answer to two decimal places.
A)0.68
B) 
C)0.72
D) 
E)2.51

Accepted Answer

The answer of Use a calculator to evaluate  .Round...

Question 19

Evaluate  without using a calculator.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate  without using a calculator.
A) 
B)...

Question 20

Which of the following functions is represented by the graph below? 
A)2arccos x
B)arcsin 2x
C)arccos (x + 1)
D)2arcsin 
E)arccos

Accepted Answer

The answer of Which of the following functions is represented...

Quiz 1: Trigonometry

A security car with its spotlight on is parked meters from a warehouse.Consider θ and x as shown in the figure.Write θ as a function of x. ​ ​

Find the value of the expression.Round your result to two decimal places. ​ ​

Use an inverse function to write θ as a function of x.

Use the properties of inverse trigonometric functions to evaluate .

Find the value of the expression.Round your result to two decimal places. ​ ​

Use a calculator to evaluate .Round your answer to two decimal places.

Write an algebraic expression that is equivalent to .

Which of the following functions is represented by the graph below?

Find the exact value of .

Find the value of the expression.Round your result to two decimal places. ​ ​

Which of the following can be inserted to make the statement true?

Write an algebraic expression that is equivalent to .

Find the value of the expression.Round your result to two decimal places. ​ ​

Find the exact value of .

Evaluate without using a calculator.

Use the properties of inverse trigonometric functions to evaluate .

Use an inverse function to write θ as a function of x.

Use a calculator to evaluate .Round your answer to two decimal places.

Evaluate without using a calculator.

Which of the following functions is represented by the graph below?

A security car with its spotlight on is parked meters from a warehouse.Consider θ and x as shown in the figure.Write θ as a function of x.

Find the value of the expression.Round your result to two decimal places.

Find the value of the expression.Round your result to two decimal places.

Find the value of the expression.Round your result to two decimal places.

Find the value of the expression.Round your result to two decimal places.