# unit circle definitions of sine and cosine   34 videos

• #### Calculating Coordinates in the Unit Circle

##### GeometryPythagorean Theorem

How to describe the unit circle. How to draw the unit circle and label its parts. How to strategize about finding coordinates on the unit circle.

graphing a rational expression 1/x asymptotes
• #### Locus and Definition of a Circle and Sphere

##### GeometryCircles

How to define a circle and a sphere using the word locus.

locus set of points distance plane circle sphere given
• #### The Law of Sines

##### GeometryBasic Trigonometry

How to define the law of sines.

law of sines ratios triangles
• #### The Law of Cosines

##### GeometryBasic Trigonometry

How to define and use the law of cosines.

law of cosines ratios triangles
• #### Area of Circles

##### GeometryArea

How to derive the formula to calculate the area of a circle.

• #### Equation of a Circle

##### GeometryPythagorean Theorem

How to derive the equation for a circle using the distance formula.

• #### Parts of a Circle

##### GeometryGeometry Building Blocks

How to define a circle and identify its main parts.

center chord diameter radius congruent circles concentric circles arc minor arc major arc semicircle central angle
• #### Writing a Good Definition

##### GeometryGeometry Building Blocks

How to write a good definition that does not have a counterexample.

definition counterexample classify quantify parallelogram
• #### Regions Between Circles and Squares

##### GeometryArea

How to calculate the area between a square and an inscribed circle.

• #### Trigonometric Ratios: Cosine

##### GeometryBasic Trigonometry

How to define the cosine ratio and identify the cosine of an angle in a right triangle.

trigonometry ratio right triangle sine SOH CAH TOA
• #### Trigonometric Ratios: Sine

##### GeometryBasic Trigonometry

How to define the sine ratio and identify the sine of an angle in a right triangle.

trigonometry ratio right triangle sine SOH CAH TOA
• #### Tangent Segments to a Circle

##### GeometryCircles

How to find the length of tangent segments drawn to a circle from the same point.

tangent congruent segments inscribed circle
• #### Circumscribed and Inscribed Circles and Polygons

##### GeometryConstructions

How to define circumscribed and inscribed circles and polygons relative to each other.

vertex radius polygon inscribed circle circumscribed
• #### Similar Triangles in Circles and Right Triangles

##### GeometrySimilarity

How to determine if two triangles in a circle are similar and how to prove that three similar triangles exist in a right triangle with an altitude.

similar inscribed angles intercepted arc right angle circle
• #### Using Sine to Calculate the Area of a Triangle

##### GeometryBasic Trigonometry

How to calculate the area of any triangle using two sides and an included angle.

area of a triangle sine
• #### Counterexample

##### GeometryGeometry Building Blocks

How to use a counterexample to prove a definition or conjecture incorrect.

counterexample definition conjecture
• #### Chords and a Circle's Center

##### GeometryCircles

How to define a chord; how to describe the effect of a perpendicular bisector of a chord and the distance from the center of the circle.

chord perpendicular bisector distance from the center congruent chords
• #### Perimeter

##### GeometryGeometry Building Blocks

How to define perimeter and calculate it for squares, rectangles, and circles.

perimeter of a square rectangle and circle
• #### Cyclic Quadrilaterals and Parallel Lines in Circles

##### GeometryCircles

How to prove that opposite angles in a cyclic quadrilateral are congruent; how to prove that parallel lines create congruent arcs in a circle.

inscribed angles cyclic quadrilaterals parallel lines alternate interior angles
• #### Inverse Trigonometric Functions

##### GeometryBasic Trigonometry

How to use inverse trig functions to find angles in right triangles.

trigonometry right triangle inverse sine cosine tangent