AMC12 Trigonometry & Precalculus 2

Question 1

What is tan(45) + tan(225)?

Accepted Answer

2

Answer

tan has period 180, so tan(225)=tan(45)=1; sum=1+1=2.

Question 2

Which expression equals sin^2(x) + cos^2(x)?

Accepted Answer

1

Answer

This is the fundamental Pythagorean identity: sin^2(x)+cos^2(x)=1 for all x.

Question 3

What is the maximum value of y = 2cos(x) - 1?

Accepted Answer

1

Answer

cos(x) achieves maximum 1, giving y_max=2(1)-1=1.

Question 4

In a triangle with a=7, b=8, and angle C=60, what is the area?

Accepted Answer

14sqrt(3)

Answer

Area=(1/2)*a*b*sin(C)=(1/2)(7)(8)(sqrt(3)/2)=14sqrt(3).

Question 5

What is sin(pi/4) * cos(pi/4)?

Accepted Answer

1/2

Answer

(sqrt(2)/2)*(sqrt(2)/2)=2/4=1/2.

AMC12 - American Mathematics Competition 12 Practice Test