# Precalculus Questions and Answers

Q: how to find tan?

A: The easiest way to find the tangent of an angle is to use a scientific or graphing calculator. However, you can also use the tangent function on a right triangle. To do this, you would take the length of the side opposite the angle you are finding the tangent of and divide it by the length of the side adjacent to the angle.

Q: how to find direction of a vector?

A: The direction of a vector is the direction of the line segment that the vector points from its tail to its head.

Q: how to find theoretical probability?

A: Theoretical probability can be found by using the ratio of the number of ways the event can occur compared to the total number of possible outcomes.

Q: how to do compositions of functions?

A: There are many ways to do function composition, but one common way is to use the composition operator (∘). This operator takes two functions as input and returns a new function that is the composition of the input functions.

Q: what is the probability of an event that is certain?

A: The probability of an event that is certain is 1.

Q: how to find experimental probability?

A: To find experimental probability, you need to find the ratio of the number of times an event occurs to the total number of trials.

Q: how to do composite functions?

A: There is no one definitive way to do composite functions. However, one common approach is to first identify the inner function and then the outer function. The inner function is typically evaluated first, and the result is then passed to the outer function.

Q: how to find angles between vectors?

A: There are a few ways to find the angle between two vectors. One way is to use the dot product. The dot product of two vectors is equal to the magnitude of the first vector times the magnitude of the second vector times the cosine of the angle between the two vectors. Another way to find the angle between two vectors is to use the cross product. The cross product of two vectors is equal to the magnitude of the first vector times the magnitude of the second vector times the sine of the angle between the two vectors.

Q: what is sin of pi?

A: Sin of pi is 0.

Q: what is the probability of a family with six children having three boys and three girls?

A: ?

A: The probability of a family with six children having three boys and three girls is 1/4 or 25%.

Q: what is a position vector?

A: A position vector is a vector that indicates the position of a point in space.

Q: what is a composite function?

A: A composite function is a function that is made up of two or more other functions.

Q: what is an inconsistent equation?

A: An inconsistent equation is one that cannot be solved.

Q: what is the flux?

A: Flux is a measure of the flow of energy or particles across a given surface.

Q: what is a normal vector?

A: A normal vector is a vector that is perpendicular to a given surface or plane.

Q: how to graph complex numbers?

A: To graph a complex number, we can plot its real and imaginary parts on a coordinate plane.

Q: how to find the length of a vector?

A: The length of a vector can be found by taking the square root of the sum of the squares of its components.

Q: how to find indicated probability?

A: There is no one definitive way to find indicated probability. However, some methods that could be used include looking at historical data, using statistical models, or conducting surveys.

Q: what is the derivative of cot?

A: The derivative of cot is csc^2.

Q: if two events are mutually exclusive, what is the probability that both occur at the same time?

A: ?

A: If two events are mutually exclusive, then the probability that both occur at the same time is zero.

Q: what does cot equal?

A: Cot equals 1 over tan.

Q: how to find an orthogonal vector?

A: An orthogonal vector can be found by taking the cross product of two vectors.

Q: what is stochastic modeling?

A: Stochastic modeling is a method of modeling that uses randomness to make predictions or simulate events.

Q: how to graph greater than or equal to?

A: The boundary line for “greater than or equal to” is a solid line. Anything above the boundary line is included in the solution, so you would shade above the boundary line.

Q: how to find tan a?

A: To find tan a, divide the length of the side opposite angle a by the length of the side adjacent to angle a.

Q: how to find length of vector?

A: The length of a vector can be found by taking the square root of the sum of the squares of the vector’s components.

Q: in a family of seven children, what is the probability of obtaining all boys?

A: ?

A: The probability of obtaining all boys is 1/128.

Q: what is classical probability?

A: Classical probability is a branch of mathematics that deals with the analysis of random phenomena. The classical approach to probability is based on the concept of an underlying physical reality that is governed by well-defined laws.

Q: what quadrant is cos negative?

A: Quadrant 3 is cos negative.

Q: how to find the experimental probability?

A: Experimental probability is found by conducting an experiment and observing the results.

Q: how to integrate xcosx?

A: xcosx = x(cosx)

Q: how to find the theoretical probability?

A: Theoretical probability can be calculated using theoretical methods, rather than experimental data.

Q: how to find tan x?

A: The tangent of an angle is the ratio of the length of the side opposite to the angle to the length of the side adjacent to the angle.

Q: what is sin theta?

A: Sin theta is the ratio of the opposite side to the hypotenuse in a right angled triangle.

Q: what is (e^x)^2?

A: (e^x)^2 = e^(2x)

Q: how to find e(xy)?

A: e(xy) = x^2y^2

Q: how to find terms?

A: The formula for finding terms is nth term = a + (n – 1)d.

Q: how to determine if a set of vectors is linearly independent?

A: A set of vectors is linearly independent if no vector in the set can be expressed as a linear combination of the other vectors in the set.

Q: how to find radius of convergence of a power series?

A: The radius of convergence of a power series is the distance from the center of the series to the nearest point where the series diverges.