Unit Circle (Trig Functions)
Videos and lessons with examples and solutions to help High School students explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
Common Core: HSF-TF.A.2
Unit Circle Definition of Trig Functions
Extending SOH CAH TOA so that we can define trig functions for a broader class of angles.
Trigonometric Functions and the Unit Circle - Conceptual Introduction
This video gives an introduction to how we use the unit circle to define sine and cosine for angles greater than 90 degrees. This is a conceptual discussion.
The main ideas are:
1) For every angle θ, the point on the unit circle is (cos θ, sin θ).
2) We can draw triangles to find out exactly what that point is.
3) Different quadrants affect the sign (negative/positive) of that point, and thus affect whether cos θ or sin θ are negative or positive.
Relationship of Sine and Cosine to the Unit Circle.
Rotate the blue arrow around the unit circle. The distance travelled from the point (1,0) to a point (, ) on a unit circle corresponds to the angle in radians between the positive axis and the line segment from the origin to the point (, ). The coordinate corresponds to the cosine of the angle and the coordinate corresponds to the sine of the angle. You can also see the angle in degrees.
Trigonometry: Unit Circle
The unit circle plays a key role in understanding how circles and triangles are connected, as well as providing a simple way to introduce the basic trigonometric functions (sine, cosine and tangent). This video describes the unit circle very carefully with the goals of providing basic insights into trigonometry and revealing the motivations behind learning the unit circle. Emphasis is placed on understanding rather than memorization.
Unit Circle F.TF.2
Use the unit circle to extend trigonometric functions to all real numbers using the radian measures of angles around it.
Extending Trigonometric Functions Beyond the Unit Circle F.TF.2
Using the unit circle idea, find the trigonometric values for any point in coordinate space.
The Reference Angle is the acute angle formed by the terminal side of the given angle and the x-axis.
Unit Circle Definition of Trig Functions
Extending SOH CAH TOA so that we can define trig functions for a broader class of angles.
Trigonometric Functions and the Unit Circle - Conceptual Introduction
This video gives an introduction to how we use the unit circle to define sine and cosine for angles greater than 90 degrees. This is a conceptual discussion.
The main ideas are:
1) For every angle θ, the point on the unit circle is (cos θ, sin θ).
2) We can draw triangles to find out exactly what that point is.
3) Different quadrants affect the sign (negative/positive) of that point, and thus affect whether cos θ or sin θ are negative or positive.
Relationship of Sine and Cosine to the Unit Circle.
Rotate the blue arrow around the unit circle. The distance travelled from the point (1,0) to a point (, ) on a unit circle corresponds to the angle in radians between the positive axis and the line segment from the origin to the point (, ). The coordinate corresponds to the cosine of the angle and the coordinate corresponds to the sine of the angle. You can also see the angle in degrees.
Relationship of Sine and Cosine to the Unit Circle from the Wolfram Demonstrations Project by Noel Patson
Trigonometry: Unit Circle
The unit circle plays a key role in understanding how circles and triangles are connected, as well as providing a simple way to introduce the basic trigonometric functions (sine, cosine and tangent). This video describes the unit circle very carefully with the goals of providing basic insights into trigonometry and revealing the motivations behind learning the unit circle. Emphasis is placed on understanding rather than memorization.
Unit Circle F.TF.2
Use the unit circle to extend trigonometric functions to all real numbers using the radian measures of angles around it.
Extending Trigonometric Functions Beyond the Unit Circle F.TF.2
Using the unit circle idea, find the trigonometric values for any point in coordinate space.
The Reference Angle is the acute angle formed by the terminal side of the given angle and the x-axis.
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