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Interactive Unit Circle

The unit circle is a fundamental concept in mathematics, used extensively in trigonometry, calculus, and beyond. It is defined as a circle with a radius of 1 unit, centered at the origin of a coordina ...

Trigonometric Ratios on the Unit Circl? At grade

This lesson explores how to find the exact trig values of certain angles.

It is an educational content of CK-12 Foundation (to access some of the CK-12 contents you must be logged in).

Putting it all Togethe? At grade

This lesson covers how to change the amplitude and translate a sine or cosine curve.

It is an educational content of CK-12 Foundation (to access some of the CK-12 contents you must be logged in).

Introduction to the Unit Circle and Radian Measur? At grade

This lesson introduces the unit circle and radians.

It is an educational content of CK-12 Foundation (to access some of the CK-12 contents you must be logged in).

Trigonometric Identities

"Identities are equations true for any value of the variable. Since a right triangle drawn in the unit circle has a hypotenuse of length 1, we define the trigonometric identies x=cos(theta) and y=sin( ...

Tangent Function Graph

"For a tangent function graph, create a table of values and plot them on the coordinate plane. Since tan(theta)=y/x, whenever x=0 the tangent function is undefined (dividing by zero is undefined). Th ...

Tangent Function

"In right triangle trigonometry (for acute angles only), the tangent is defined as the ratio of the opposite side to the adjacent side. The unit circle definition is tan(theta)=y/x or tan(theta)=sin(t ...

Solving Trigonometric Equations

"When solving trigonometric equations, we find all the angles that make the equation true. If there is no interval given, use periodicity to show the infinite number of solutions. Two ways to visuali ...

Factoring Trigonometric Equations

"Solving second degree trig functions can be accomplished by factoring polynomials into products of binomials. When factoring trigonometric equations, we can use the zero product property to set up tw ...

Sine Definition

"The right triangle definitions of sine and cosine only apply to acute angles, so a more complete definition is needed. The point where the terminal side intersects the unit circle (x, y) is the basi ...

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