Trigonometric Expansions and Summations - One Line Questions
1.
If A+B+C = pi, what is the value of cos(A+B+C)? —
-1
2.
What is the sum-to-product formula for cosC - cosD? —
-2 sin((C+D)/2) sin((C-D)/2)
3.
The expression sin^2 A is related to cos(2A) by: —
(1 - cos(2A)) / 2
4.
The expression cos^2 A is related to cos(2A) by: —
(1 + cos(2A)) / 2
5.
What is the expansion of tan(3A)? —
(3 tanA - tan^3 A) / (1 - 3 tan^2 A)
6.
What is the value of sin(15 degrees) using sum/difference formulas? —
(sqrt(6) - sqrt(2)) / 4
7.
What is the value of cos(75 degrees) using sum/difference formulas? —
(sqrt(6) - sqrt(2)) / 4
8.
Expand tan(A-B). —
(tanA - tanB) / (1 + tanA tanB)
9.
What is the expansion of tan(A+B+C)? —
(tanA + tanB + tanC - tanA tanB tanC) / (1 - tanA tanB - tanB tanC - tanC tanA)
10.
What is the expansion of tan(A+B)? —
(tanA + tanB) / (1 - tanA tanB)
11.
What is the expansion of sin(A+B+C) if A+B+C = pi? —
0
12.
If A+B+C = pi, what is the value of tan(A+B+C)? —
0
13.
What is cos(2A) in terms of sinA only? —
1 - 2 sin^2 A
14.
What is the value of tan(75 degrees) using sum/difference formulas? —
2 + sqrt(3)
15.
Express cos(2A) in terms of cosA only. —
2 cos^2 A - 1
16.
What is the sum-to-product formula for cosC + cosD? —
2 cos((C+D)/2) cos((C-D)/2)
17.
Express sinC - sinD using sum-to-product formulas. —
2 cos((C+D)/2) sin((C-D)/2)
18.
What is the formula for cos(A+B) + cos(A-B)? —
2 cosA cosB
19.
What is the formula for sin(A+B) - sin(A-B)? —
2 cosA sinB
20.
What is the sum-to-product formula for sinC + sinD? —
2 sin((C+D)/2) cos((C-D)/2)
21.
What is the value of sin(2A) in terms of sinA and cosA? —
2 sinA cosA
22.
What is the formula for sin(A+B) + sin(A-B)? —
2 sinA cosB
23.
What is the formula for cos(A-B) - cos(A+B)? —
2 sinA sinB
24.
Expand tan(2A). —
2 tanA / (1 - tan^2 A)
25.
What is the expansion of sin(3A)? —
3 sinA - 4 sin^3 A
26.
Expand cos(3A). —
4 cos^3 A - 3 cosA
27.
What is the expansion of cos(nA) for integer n? —
A power series in cosA and sinA
28.
What is the expansion of sin(nA) for integer n? —
A power series in sinA and cosA
29.
What is the sum of angles in the numerator of the tan(A+B+C) expansion? —
A+B+C
30.
What is the sum of angles in the denominator of the tan(A+B+C) expansion? —
AB+BC+CA
31.
The sum ∑_{k=1}^{n} sin(kx) can be evaluated using: —
Complex exponentials or product-to-sum identities
32.
The sum ∑_{k=1}^{n} cos(kx) can be evaluated using: —
Complex exponentials or product-to-sum identities
33.
Expand cos(2A) using both sinA and cosA. —
cos^2 A - sin^2 A
34.
What is the product-to-sum formula for 2 sinA sinB? —
cos(A-B) - cos(A+B)
35.
What is the formula for 2 cosA cosB? —
cos(A+B) + cos(A-B)
36.
Expand cos(A+B). —
cosA cosB + sinA sinB
37.
What is the expansion of cos(A-B)? —
cosA cosB + sinA sinB
38.
Expand cos(A+B+C). —
cosA cosB cosC - cosA sinB sinC - sinA cosB sinC - sinA sinB cosC
39.
The expansion of sin(A+B+C) involves how many product terms of sines and cosines? —
Four
40.
The expansion of cos(A+B+C) involves how many product terms of sines and cosines? —
Four
41.
What is the general formula for sin(nA) in terms of sinA and cosA, using De Moivre's theorem? —
Im( (cosA + i sinA)^n )
42.
What is the general formula for cos(nA) in terms of sinA and cosA, using De Moivre's theorem? —
Re( (cosA + i sinA)^n )
43.
Express 2 cosA sinB as a sum or difference. —
sin(A+B) - sin(A-B)
44.
What is the product-to-sum formula for 2 sinA cosB? —
sin(A+B) + sin(A-B)
45.
Expand sin(A-B). —
sinA cosB - cosA sinB
46.
What is the value of sin(A+B) expanded? —
sinA cosB + cosA sinB
47.
What is the formula for sin(A+B+C)? —
sinA cosB cosC + cosA sinB cosC + cosA cosB sinC - sinA sinB sinC
48.
If A+B+C = pi, what is the relation between tangents of the angles? —
tanA + tanB + tanC = tanA tanB tanC
49.
The expansion of sin(A+B+C) uses the identity: sin(X+Y) = sinXcosY + cosXsinY, where X=A and Y=B+C. —
True
50.
The expansion of cos(A+B+C) uses the identity: cos(X+Y) = cosXcosY - sinXsinY, where X=A and Y=B+C. —
True