Q. If x = sin^(-1)(-1/2), then what is the value of x?
-
A.
-π/6
-
B.
π/6
-
C.
-π/3
-
D.
π/3
Solution
sin^(-1)(-1/2) = -π/6, since sin(-π/6) = -1/2.
Correct Answer: A — -π/6
Learn More →
Q. If x = sin^(-1)(-1/2), what is the value of x?
-
A.
-π/6
-
B.
π/6
-
C.
π/4
-
D.
0
Solution
sin^(-1)(-1/2) = -π/6, since sin(-π/6) = -1/2.
Correct Answer: A — -π/6
Learn More →
Q. If x = sin^(-1)(1/2), what is the value of cos(x)?
Solution
If x = sin^(-1)(1/2), then x = π/6. Therefore, cos(x) = cos(π/6) = √3/2.
Correct Answer: B — √3/2
Learn More →
Q. If x = sin^(-1)(1/3), then what is the value of cos^(-1)(√(1 - (1/3)^2))?
-
A.
π/3
-
B.
π/2
-
C.
2π/3
-
D.
π/4
Solution
Using the identity cos^(-1)(√(1 - sin^2(x))) = π/2 - x, we find that cos^(-1)(√(1 - (1/3)^2)) = π/2 - sin^(-1)(1/3).
Correct Answer: B — π/2
Learn More →
Q. If x = sin^(-1)(1/√2), then what is the value of cos(x)?
-
A.
1/2
-
B.
√2/2
-
C.
√3/2
-
D.
1
Solution
If x = sin^(-1)(1/√2), then sin(x) = 1/√2. Therefore, cos(x) = √(1 - sin^2(x)) = √(1 - (1/√2)^2) = √(1/2) = √2/2.
Correct Answer: B — √2/2
Learn More →
Q. If x = sin^(-1)(1/√2), then what is the value of cos^(-1)(x)?
-
A.
π/4
-
B.
π/3
-
C.
π/2
-
D.
π/6
Solution
Since x = sin^(-1)(1/√2) = π/4, then cos^(-1)(x) = π/2 - π/4 = π/4.
Correct Answer: A — π/4
Learn More →
Q. If x = sin^(-1)(3/5), what is cos(x)?
-
A.
4/5
-
B.
3/5
-
C.
5/4
-
D.
1/5
Solution
Using the identity cos^2(x) + sin^2(x) = 1, we find cos(x) = √(1 - (3/5)^2) = 4/5.
Correct Answer: A — 4/5
Learn More →
Q. If x = sin^(-1)(3/5), what is the value of cos(x)?
-
A.
4/5
-
B.
3/5
-
C.
2/5
-
D.
1/5
Solution
Using the identity cos(x) = sqrt(1 - sin^2(x)), we have cos(x) = sqrt(1 - (3/5)^2) = sqrt(16/25) = 4/5.
Correct Answer: A — 4/5
Learn More →
Q. If x = tan^(-1)(1), what is the value of x?
-
A.
π/4
-
B.
π/3
-
C.
π/6
-
D.
0
Solution
tan^(-1)(1) = π/4, since tan(π/4) = 1.
Correct Answer: A — π/4
Learn More →
Q. If x = tan^(-1)(√3), then what is the value of sin^(-1)(x)?
-
A.
π/3
-
B.
π/4
-
C.
π/2
-
D.
π/6
Solution
x = tan^(-1)(√3) = π/3, thus sin^(-1)(x) = sin^(-1)(√3/2) = π/3.
Correct Answer: A — π/3
Learn More →
Q. If x = tan^(-1)(√3), what is the value of sin(2x)?
-
A.
√3/2
-
B.
1
-
C.
√2/2
-
D.
0
Solution
Since tan^(-1)(√3) = π/3, then 2x = 2π/3 and sin(2x) = sin(2π/3) = √3/2.
Correct Answer: B — 1
Learn More →
Q. If x^2 + 2x + 1 = 0, what is the value of x?
Solution
This is a perfect square: (x + 1)^2 = 0 => x = -1.
Correct Answer: A — -1
Learn More →
Q. If x^2 - 6x + 9 = 0, what is the value of x?
Solution
This is a perfect square: (x - 3)^2 = 0, so x = 3.
Correct Answer: A — 3
Learn More →
Q. If y = cos^(-1)(1/2), what is the value of y?
-
A.
π/3
-
B.
π/4
-
C.
π/6
-
D.
π/2
Solution
cos^(-1)(1/2) = π/3, since cos(π/3) = 1/2.
Correct Answer: A — π/3
Learn More →
Q. If y = cos^(-1)(x), then what is dy/dx?
-
A.
-1/√(1-x^2)
-
B.
1/√(1-x^2)
-
C.
1/x
-
D.
-1/x
Solution
The derivative of y = cos^(-1)(x) is dy/dx = -1/√(1-x^2).
Correct Answer: A — -1/√(1-x^2)
Learn More →
Q. If y = cos^(-1)(x), what is dy/dx?
-
A.
-1/√(1-x^2)
-
B.
1/√(1-x^2)
-
C.
0
-
D.
1
Solution
The derivative of cos^(-1)(x) is dy/dx = -1/√(1-x^2).
Correct Answer: A — -1/√(1-x^2)
Learn More →
Q. If y = sin^(-1)(x), what is dy/dx?
-
A.
1/sqrt(1-x^2)
-
B.
1/(1-x^2)
-
C.
sqrt(1-x^2)
-
D.
1/x
Solution
The derivative of y = sin^(-1)(x) is dy/dx = 1/sqrt(1-x^2).
Correct Answer: A — 1/sqrt(1-x^2)
Learn More →
Q. If z = 1 + i, find the conjugate of z.
-
A.
1 - i
-
B.
1 + i
-
C.
-1 + i
-
D.
-1 - i
Solution
The conjugate of z = 1 + i is z̅ = 1 - i.
Correct Answer: A — 1 - i
Learn More →
Q. If z = 1 + i, find the value of z^3.
-
A.
-2 + 2i
-
B.
2 + 2i
-
C.
0
-
D.
1 + 3i
Solution
z^3 = (1 + i)^3 = 1 + 3i - 3 - i = -2 + 2i.
Correct Answer: A — -2 + 2i
Learn More →
Q. If z = 1 + i, find the value of z^4.
Solution
z^4 = (1 + i)^4 = (2e^(iπ/4))^4 = 16e^(iπ) = -16.
Correct Answer: A — -4
Learn More →
Q. If z = 1 + i, find z^2.
-
A.
2i
-
B.
2
-
C.
1 + 2i
-
D.
0
Solution
z^2 = (1 + i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i.
Correct Answer: C — 1 + 2i
Learn More →
Q. If z = 1 + i, find z^3.
-
A.
-2 + 2i
-
B.
2 + 2i
-
C.
0
-
D.
1 + i
Solution
z^3 = (1 + i)^3 = 1 + 3i - 3 - i = -2 + 2i.
Correct Answer: A — -2 + 2i
Learn More →
Q. If z = 1 + i, find z^4.
Solution
z^4 = (1 + i)^4 = 4i.
Correct Answer: A — -4
Learn More →
Q. If z = 1 + i, what is z^2?
-
A.
2i
-
B.
2
-
C.
1 + 2i
-
D.
0
Solution
z^2 = (1 + i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i.
Correct Answer: C — 1 + 2i
Learn More →
Q. If z = 1 + i√3, find the argument of z.
-
A.
π/3
-
B.
2π/3
-
C.
π/6
-
D.
5π/6
Solution
The argument θ = tan^(-1)(√3/1) = π/3.
Correct Answer: A — π/3
Learn More →
Q. If z = 1 + i√3, find the modulus of z.
Solution
|z| = √(1^2 + (√3)^2) = √(1 + 3) = √4 = 2.
Correct Answer: A — 2
Learn More →
Q. If z = 1 + i√3, find the value of |z|^2.
Solution
|z|^2 = (1)^2 + (√3)^2 = 1 + 3 = 4.
Correct Answer: A — 4
Learn More →
Q. If z = 1 + i√3, find |z|.
Solution
|z| = √(1^2 + (√3)^2) = √(1 + 3) = √4 = 2.
Correct Answer: A — 2
Learn More →
Q. If z = 1 + i√3, find |z|^2.
Solution
|z|^2 = (1)^2 + (√3)^2 = 1 + 3 = 4.
Correct Answer: A — 4
Learn More →
Q. If z = 1 + i√3, then the argument of z is?
-
A.
π/3
-
B.
π/6
-
C.
2π/3
-
D.
5π/6
Solution
The argument θ = tan^(-1)(√3/1) = π/3.
Correct Answer: A — π/3
Learn More →
Showing 421 to 450 of 862 (29 Pages)
