AMC12 Trigonometry & Precalculus

Question 1

What is sin(30) + cos(60)?

Accepted Answer

1

Answer

sin(30)=1/2 and cos(60)=1/2, so their sum is 1.

Question 2

In a right triangle, tan(theta)=3/4. What is sin(theta)?

Accepted Answer

3/5

Answer

Opposite=3, adjacent=4, hypotenuse=5, so sin(theta)=3/5.

Question 3

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

Accepted Answer

2pi/3

Answer

The period is 2pi/|b|=2pi/3.

Question 4

What is cos(135 degrees)?

Accepted Answer

-sqrt(2)/2

Answer

135 is in Q2 where cosine is negative; cos(135)=-cos(45)=-sqrt(2)/2.

Question 5

If sin(x)=0.6 with x in the first quadrant, what is tan(x)?

Accepted Answer

3/4

Answer

cos(x)=sqrt(1-0.36)=0.8, so tan(x)=0.6/0.8=3/4.

AMC12 - American Mathematics Competition 12 Practice Test