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114 | eureka Math algebra II Study guIde
● (^) A Square root of a Number A square root of a number x is a number whose square is x.
In symbols, a square root of x is a number a such that ax^2 =. Negative numbers do
not have any real square roots, zero has exactly one real square root, and positive
numbers have two real square roots.
● (^) The Square root of a Number Every positive real number x has a unique positive square
root called the square root or principal square root of x; it is denoted x. The square root
of zero is zero.
● (^) Vertex of a Parabola The vertex of a parabola is the point where the axis of symmetry
intersects the parabola.
Module 2
● (^) Amplitude The amplitude is the distance between a maximal point of the graph of the
sinusoidal function and the midline.
● (^) Cosecant Let θ be any real number such that q¹kp for all integers k. In the Cartesian
plane, rotate the initial ray by θ radians about the origin. Intersect the resulting terminal
ray with the unit circle to get a point (xθ, yθ). The value of csc(θ) is y^1 q.
● (^) Cosine Let θ be any real number. In the Cartesian plane, rotate the initial ray by θ radians
about the origin. Intersect the resulting terminal ray with the unit circle to get a point
(xθ, yθ). The value of cos(θ) is xθ.
● (^) Cotangent Let θ be any real number such that q¹kp for all integers k. In the Cartesian
plane, rotate the initial ray by θ radians about the origin. Intersect the resulting terminal
ray with the unit circle to get a point (xθ, yθ). The value of cot(θ) is xyqq.
● (^) Frequency The frequency of a periodic function is the unit rate of the constant rate
defined by the number of cycles per unit length.
● (^) Midline The midline is the horizontal line that is halfway between the maximal line and
the minimal line.
● (^) Period The period P is the distance between two consecutive maximal points or two
consecutive minimal points on the graph of a sinusoidal function.
● (^) Periodic Function A function f whose domain is a subset of the real numbers is said to be
periodic with period P> 0 if the domain of f contains xP+ whenever it contains x, and if
fx()+=Pf()x for all real numbers x in its domain.
● (^) radian A radian angle is the angle subtended by an arc of a circle that is equal in length
to the radius of the circle. A radian (1 rad) is a unit of rotational measure given by a
rotation by a radian angle.
● (^) Secant Let θ be any real number such that q¹+p 2 kp for all integers k. In the Cartesian
plane, rotate the initial ray by θ radians about the origin. Intersect the resulting terminal
ray with the unit circle to get a point (xθ, yθ). The value of sec(θ) is x^1 q.
● (^) Sine Let θ be any real number. In the Cartesian plane, rotate the initial ray by θ radians
about the origin. Intersect the resulting terminal ray with the unit circle to get a point
(xθ, yθ). The value of sin(θ) is yθ.
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