Multi Choice Problems

Question 1 of 20
5.0/ 5.0 Points
Use the given information to find the exact value of the expression.

sin α = , α lies in quadrant II, and cos β = , β lies in quadrant I Find sin (α – β).

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A.  
B.  
C.  
D.  

Question 2 of 20
0.0/ 5.0 Points
Solve the equation on the interval [0, 2π).

tan2x sin x = tan2x

A. 0,  
B. , 2π  
C. , π  
D. 0, π  

Question 3 of 20
0.0/ 5.0 Points
The sound produced by touching each button on a touch-tone phone is described by y = sin 2πlt + sin 2πht where l and h are the low and high frequencies (cycles per seconD. in the figure shown.

Use a calculator to find the graph of the sound emitted by touching the 4 key in a [0, 0.01, 0.001] by [-2, 2, 1] viewing rectangle.

A.  
B.  
C.  
D.  

Question 4 of 20
0.0/ 5.0 Points
Solve the equation on the interval [0, 2π).

cos x + 2 cos x sin x = 0

A. 0, , ,  
B. , , ,  
C. , , 2π  
D. ,  

Question 5 of 20
0.0/ 5.0 Points
Rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.

cos3x

A. cos x + cos 3x + cos 2x  
B. cos x + cos 3x  
C. cos x – cos 3x  
D. cos x – cos 3x – cos 2x  

Question 6 of 20
0.0/ 5.0 Points
Rewrite the expression in terms of the given function or functions. (sec x + csc x) (sin x + cos x) – 2 – cot x; tan x

A. 0  
B. 2tan x  
C. tan x  
D. 2 + tan x  

Question 7 of 20
0.0/ 5.0 Points
Complete the identity. = ?

A. cot α + cot β  
B. tan β + tan α  
C. tan α + tan β  
D. -tan α + cot β  

Question 8 of 20
5.0/ 5.0 Points
Solve the equation on the interval [0, 2π).

sec = cos

A. , , , , , ,  
B. 0  
C. ,  
D. 0, , π,  

Question 9 of 20
0.0/ 5.0 Points
The weekly sales in thousands of items of a product has a seasonal sales record approximated by (t is time in weeks with t = 1  referring to the first week in the year). During which week(s) will the sales equal 96,990 items?

A. week 4, week 20, and week 52  
B. week 21 and week 30  
C. week 4 and week 47  
D. week 30 and week 47  

Question 10 of 20
0.0/ 5.0 Points
Find the exact value of the expression.

sin 265° cos 25° – cos 265° sin 25°

A. –  
B. –  
C.  
D.  

Question 11 of 20
5.0/ 5.0 Points
Find all solutions of the equation.

5 sin x – 8 = 3 sin x- 7

A. x = + nπ or x = + nπ  
B. x = + nπ or x = + nπ  
C. x = + 2nπ or x = + 2nπ  
D. x = + 2nπ or x = + 2nπ  

Question 12 of 20
0.0/ 5.0 Points
Write the expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression.

2 sin 120° cos 120°

A. –  
B.  
C.  
D.  

Question 13 of 20
0.0/ 5.0 Points
Complete the identity. sin4x – cos4x = ?

A. 1 – 2cos2 x  
B. 1 – 2sin2 x  
C. 1 + 2sin2 x  
D. 1 + 2cos2 x  

Question 14 of 20
0.0/ 5.0 Points
Complete the identity. = ?

A. 1 + cot α cot β  
B. tan α tan β + cot β  
C. 1 + tan α tan β  
D. 1 + cot α tan β  

Question 15 of 20
5.0/ 5.0 Points
Use the given information to find the exact value of the expression.

sin θ = , θ lies in quadrant II Find tan 2θ.

A. –  
B.  
C. –  
D.  

Question 16 of 20
5.0/ 5.0 Points
Use a calculator to solve the equation on the interval [0, 2π). Round to the nearest hundredth of a radian. sin 2x – sin x = 0

A. 1.05, 3.14, 5.24  
B. 0, 1.05, 3.14, 5.24  
C. 0, 2.09, 3.14, 4.19  
D. 0, 2.09, 4.19  

Question 17 of 20
5.0/ 5.0 Points
Express the sum or difference as a product. sin 4x – sin 6x

A. 2 cos 4x cos 5x  
B. 2 sin 5x cos x  
C. -2 sin x cos 5x  
D. -2 sin x  

Question 18 of 20
0.0/ 5.0 Points
Solve the equation on the interval [0, 2π).

sin2 x – cos2x = 0

A.  
B. ,  
C. ,  
D. ,, ,  

Question 19 of 20
0.0/ 5.0 Points
Show that the equation is not an identity by finding a value of x for which both sides are defined but not equal. cos x – cos x sinx = cos3x

A. π  
B. 0  
C.  
D.  

Question 20 of 20
5.0/ 5.0 Points
Complete the identity. = ?

A. cot α + cot β  
B. tan α + tan β  
C. tan β + tan α  
D. -tan α + cot β  

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