Circle Theorem + Triangle Key Notes

How do you find the length of a sector in a circle?

The length of a sector in a circle can be found by using the formula:

(arc length)/circle circumference = (central angle in degrees)/360 degrees

How do you find the area of a sector in a circle?

The area of a sector in a circle can be found by using the formula: (sector area)/circle area = (central angle in degrees)/360degrees

The sin of an angle is equal to what?

The sin of an angle is equal to the cosine of the same complementary angle. For example, sin 30 is equivalent to cos60 because 30+60 = 90

Are trigonometric ratios of similar triangles always the same?

Yes!!! Side length does not matter because it is being scaled by the same factor all around so the trigonometric ratio will remain the same.

What is the distance formula?

The distance formula is used to calculate the distance between two points. This is useful because if you are given the center of a circle and a point on the circle’s radius, but not the radius, then you can utilize the distance formula to find the radius.

What is the distance formula?

√((x₂ - x₁)² + (y₂ - y₁)²)

If given the knowledge that a circle has its center at either y=x

or x=y and a point (x,y) is on the circle then how should you solve it?

First fill out the circle equation with as much knowledge given, then plug in the points and solve.