EmSAT Mathematics Flashcards

What is the formula for the area of a circle?

Answer: πr²

The area of a circle with radius r is A = πr². The circumference (perimeter) is 2πr, not the area.

In a right triangle, if one leg is 3 and the other is 4, what is the hypotenuse?

Answer: 5

Using the Pythagorean theorem: c² = 3² + 4² = 9 + 16 = 25, so c = 5. This is the classic 3-4-5 right triangle.

What is sin(30°)?

Answer: 1/2

sin(30°) = 1/2. This is a standard trigonometric value. In a 30-60-90 triangle, the side opposite 30° is half the hypotenuse.

What does the cosine rule state?

Answer: c² = a² + b² − 2ab·cos(C)

The cosine rule is c² = a² + b² − 2ab·cos(C). It generalizes the Pythagorean theorem to non-right triangles.

Convert 90° to radians.

Answer: π/2

To convert degrees to radians, multiply by π/180. 90 × π/180 = π/2 radians.

What is tan(45°)?

Answer: 1

tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1. In a 45-45-90 triangle, both legs are equal, so the ratio is 1.