Unit 6 Test Review - Circles

Front

What is the standard form of the equation of a circle?

Back

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

Tags

CCSS.HSG.GPE.A.1

Front

How do you find the center and radius of a circle from its equation?

Back

To find the center and radius from the equation Ax² + Ay² + Bx + Cy + D = 0, rewrite it in standard form. The center is (-B/2A, -C/2A) and the radius is √((B² + C² - 4AD)/(4A²)).

Tags

CCSS.HSG.GPE.A.1

Front

What is the relationship between the radius and the arc length in a circle?

Back

The arc length (s) is given by the formula s = rθ, where r is the radius and θ is the central angle in radians.

Tags

CCSS.HSG.C.B.5

Front

What is the value of cos(0) in the unit circle?

Back

The value of cos(0) is 1.

Tags

CCSS.HSF.TF.A.2

Front

What is the value of sin(π/2) in the unit circle?

Back

The value of sin(π/2) is 1.

Tags

CCSS.HSF.TF.A.2

Front

How do you calculate the circumference of a circle?

Back

The circumference (C) of a circle is calculated using the formula C = 2πr, where r is the radius.

Tags

CCSS.7.G.B.4

Front

What is the value of cos(π/4) in the unit circle?

Back

The value of cos(π/4) is √2/2.

Tags

CCSS.HSF.TF.A.2

Front

What is the formula for the area of a circle?

Back

The area (A) of a circle is given by the formula A = πr², where r is the radius.

Tags

CCSS.7.G.B.4

Front

What is the significance of the unit circle in trigonometry?

Back

The unit circle is a circle with a radius of 1 centered at the origin, used to define trigonometric functions for all angles.

Tags

CCSS.HSF.TF.A.2

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, multiply the degree measure by π/180.

Tags

CCSS.HSF.TF.A.1