AMC 12 AMC 12 Trigonometry & Complex Numbers

Question 1

What is the value of sin(π/6)?

Accepted Answer

1/2

Answer

√3/2

Answer

√2/2

Answer

1

Question 2

What is the modulus of the complex number 3 + 4i?

Accepted Answer

5

Answer

3

Answer

4

Answer

7

Question 3

If z = 1 + i, what is z²?

Accepted Answer

2i

Answer

2

Answer

1 + 2i

Answer

-1 + 2i

Question 4

Which expression equals cos(2θ)?

Accepted Answer

2cos²(θ) − 1

Answer

2cos(θ) − 1

Answer

1 − 2cos(θ)

Answer

cos(θ) − sin(θ)

Question 5

What is the argument (principal angle) of the complex number −1 + i?

Accepted Answer

3π/4

Answer

π/4

Answer

−π/4

Answer

π/6

Question 6

What is the value of sin²(θ) + cos²(θ) for all θ?

Accepted Answer

1

Answer

0

Answer

2

Answer

sin(2θ)