Arccosine is a relationship used to find an acute angle measure in a right triangle when two side lengths are known.

The arccosine of a number between 0 and 1 is the measure of an acute angle whose cosine is that number.

Arcsine is a relationship used to find an acute angle measure in a right triangle when two side lengths are known.

The arcsine of a number between 0 and 1 is the measure of an acute angle whose sine is that number.

Arctangent is a relationship used to find an acute angle measure in a right triangle when two side lengths are known.

The arctangent of a positive number is the measure of an acute angle whose tangent is that number.

A chance experiment is something that can be done over and over again, and what will happen each time is not known.

For example, each time the spinner is spun, it could land on red, yellow, blue, or green.

The circumcenter of a triangle is the intersection point of all three perpendicular bisectors of the triangle’s sides. It is the center of the triangle’s circumscribed circle.

In this diagram, the circumcenter is point \(D\).

Completing the square is a method of rewriting a quadratic expression or equation. 

• A quadratic expression is rewritten in the form  \(a(x+p)^2-q\), where \(a\), \(p\), and \(q\) are constants and \(a\neq0.\)
• A quadratic equation is rewritten in  the form \(a(x+p)^2=q\).

A number in the complex plane. It can be written as \(a + bi\), where \(a\) and \(b\) are real numbers and \(i^2 = \text-1\).

Conditional probability is the likelihood that one event occurs given that another event occurs.

Events are called dependent when they are from the same experiment and where the outcome of one event affects the probability of another.

An event is a set of 1 or more outcomes in a chance experiment.

For example, if a number cube is rolled, there are 6 possible outcomes.

Some events are “rolling a number less than 3,” “rolling an even number,” or “rolling a 5.”

A quadratic expression is in factored form when it is written as the product of a constant times two linear factors.

• \(2x^2 + 4x - 6\) written in factored form is \(2(x-1)(x+3)\).
• \(15x^2 + x - 2\) written in factored form is \((5x + 2)(3x-1)\).

A function is a rule that takes inputs from one set and assigns them to outputs from another set. Each input is assigned exactly one output.

A number on the imaginary number line. It can be written as \(bi\), where \(b\) is a real number and \(i^2 = \text-1\).

The incenter of a triangle is the intersection point of all three of the triangle’s angle bisectors. It is the center of the triangle’s inscribed circle.

In this diagram the incenter is point \(D\).

Events are called independent when they are from the same experiment and the outcome of one event does not affect the probability of another.

An irrational number is a number that is not rational. This means it cannot be expressed as a positive fraction, a negative fraction, or zero. It cannot be written in the form \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\).

For example, the numbers \(\pi\) and \(\text{-}\sqrt{2}\) are irrational numbers.

A linear term of an expression has a variable raised to the first power. 

• In the expression, \(5x+2\), the linear term is \(5x\).
• In the expression, \(20-x^2+x\), the linear term is \(x\).
• In the expression \(ax^2+bx+c\), where \(a\), \(b\), and \(c\) are constants, the linear term is \(bx\).

An outcome of a chance experiment is one of the things that can happen.

For example, the possible outcomes of tossing a coin are heads and tails.

A perfect square is a number or an expression that is the result of multiplying a number or an expression to itself. In general, the multiplied number is rational and the multiplied expression has rational coefficients.

The probability of a chance event is a number from 0 to 1 that expresses the likelihood of the event occurring, with 0 meaning it will never occur and 1 meaning it will always occur.

A quadratic equation is an equation that is equivalent to one of the form \(ax^2 + bx + c = 0\), where \(a\), \(b\), and \(c\) are constants and \(a \neq 0\).

A quadratic expression is an expression that is equivalent to one of the form \(ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants and \(a \neq 0\).

The quadratic formula is \(x = {\text-b \pm \sqrt{b^2-4ac} \over 2a}\) and gives the solutions of the quadratic equation \(ax^2 + bx + c = 0\), where \(a\), \(b\), and \(c\) are constants and \(a \neq 0\).

A quadratic function is a function where the output is given by a quadratic expression in the input.

For example, \(f(x) =ax^2+bx+c\), where \(a\), \(b\), and \(c\) are constants and \(a\ne0\), is a quadratic function.

A radian is a unit of measurement for angles, based on the radius of a circle.

The radian measure of any central angle is this ratio: \(\frac{\text{length of intercepted arc}}{\text{radius}}\)

A rational number is a number that can be written as a positive fraction, a negative fraction, or zero. It can be written in the form \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\). 

• 0.7 is a rational number because it can be written as \(\frac{7}{10}\).
• The numbers 0, 3, \(\text{-}\frac{3}{4}\), and 6.7 are all rational numbers. 

A number on the real number line.

The sample space is the list of every possible outcome for a chance experiment.

For example, the sample space for tossing two coins is:

The standard form of a quadratic expression is \(ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants and \(a\) \(\ne\) 0.

Trigonometric ratios relate the angles and sides of right triangles.

Three trigonometric ratios are sine, cosine, and tangent.

\(\sin(\theta)=\dfrac{\text{opposite}}{\text{hypotenuse}}\)

\(\cos(\theta)=\dfrac{\text{adjacent}}{\text{hypotenuse}}\)

\(\tan(\theta)=\dfrac{\text{opposite}}{\text{adjacent}}\)

The vertex of the graph of a quadratic function or of an absolute value function is the point where the graph changes from increasing to decreasing, or vice versa. It is the highest or lowest point on the graph.

The vertex form of a quadratic expression is \(a(x-h)^2 + k\), where \(a\), \(h\), and \(k\) are constants and \(a \neq 0\). The vertex of the graph is at the point \((h,k)\).

A zero of a function is an input that results in an output of 0. In other words, if \(f(a) = 0\), then \(a\) is a zero of \(f\).

The zero product property says that if the product of two numbers is 0, then one of the numbers must be 0.