AIME Trigonometry and Complex Numbers 2

Question 1

In a right triangle, if sin(A) = 5/13, what is cos(A)?

Accepted Answer

12/13

Answer

5/12

Answer

13/12

Answer

13/5

Question 2

What is the period of f(x) = sin(3x)?

Accepted Answer

2π/3

Answer

2π

Answer

3π

Answer

6π

Question 3

Compute the conjugate of z = 7 - 2i.

Accepted Answer

7 + 2i

Answer

7 - 2i

Answer

-7 + 2i

Answer

-7 - 2i

Question 4

Simplify (2+i)/(1-i).

Accepted Answer

(1+3i)/2

Answer

(3+i)/2

Answer

(1-3i)/2

Answer

(3-i)/2

Question 5

Find all x in [0°, 360°) satisfying 2sin(x) = √2.

Accepted Answer

45° and 135°

Answer

30° and 150°

Answer

45° and 225°

Answer

60° and 120°

Question 6

If z = 1 + i, what is z^2?

Accepted Answer

2i

Answer

2

Answer

-2i

Answer

1+2i