Understanding the Unit Circle and Special Right Triangles

What is the equation of a unit circle?

• x^2 - y^2 = 0

• x^2 + y^2 = 1

• x^2 + y^2 = 0

• x^2 - y^2 = 1

In a 45-45-90 triangle, what is the ratio of the side length to the hypotenuse?

• 1 to 2

• 1 to √2

• 1 to 1

• 1 to √3

What are the coordinates of a point on the unit circle at an angle of 45 degrees?

• (√2/2, √2/2)

• (0, 1)

• (-√2/2, √2/2)

• (1, 0)

In a 30-60-90 triangle, what is the length of the side opposite the 30-degree angle if the hypotenuse is 1?

• 1

• 1/2

• √3/2

• √2/2

If the 60-degree angle is at the bottom left of a 30-60-90 triangle, what happens to the base and height?

• They remain the same

• They are swapped

• They are doubled

• They are halved