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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( ...

The Ellipse

"An ellipse is an important conic section and is formed by intersecting a cone with a plane that does not go through the vertex of a cone. The ellipse is defined by two points, each called a focus. Fr ...

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 ...

Surface Area of Joined Solids

"Surface area is a two-dimensional property of a three-dimensional figure. When solids are joined together, such as a hemisphere on a cone, the surface area of the connecting circle is not included in ...

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 ...

Evaluating Cosine

"To find the value of sine and cosine at non-acute angles (from 90 to 360), first draw the angle on the unit circle and find the reference angle. A reference angle is formed by the terminal side and ...

Conic Section Formulas

"We can easily identify a conic section by its formula. Conic section formulas have different identifiers. For example, a vertical parabola has a squared "x" term and single "y" term while a horizonta ...

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