tan θ = P / B.Įllipse - An ellipse is a curve traced by the set of all points in a plane that have a constant sum from two fixed points. Tangent Function - Tangent is the ratio of the sine function to the cosine function. sin θ = P / H.Ĭosine Function - The cosine function is the ratio of the base to the hypotenuse. Sine Function - The sine function can be defined as the ratio of the perpendicular to the hypotenuse of a right-angled triangle. The formula to calculate the area of a triangle is rac imes base imes height. y = mx + c is the general equation of a straight line, where m is the slope and c is the y-intercept.Īrea of a Triangle - Area of a triangle can be defined as the space covered within the boundary of the triangle.

Slope - The slope of a line can be defined as the gradient of the line that describes its steepness. Given below are some important concepts and formulas that cover the scope of precalculus. It helps to streamline the process of studying and preparing for a test.

u + v = (u 1+v 1, u 2+v 2, u 3+v 3), where, u = (u 1, u 2, u 3) and v = (v 1, v 2, v 3)Ī precalculus cheat sheet can be very important as it gives a complete overview of various vital concepts before an examination.

C = A + B, where c ij = a ij + b ij, where A, B and C are square matrices.

A -1A = I, where A -1 is the inverse matrix of A and I is the identity matrix.

Equation of an ellipse: x 2/a 2 + y 2 / b 2 = 1.

Equation of a hyperbola: x 2/a 2 - y 2 / b 2 = 1.

Equation of a parabola is: y = a(x - h) 2 + k or x = a(y - k) 2 + h.

Equation of a circle = (x − h) 2 + (y − k) 2 = r 2, with the center at (h, k).

Sum of n terms in a geometric sequence, S n = a (r n - 1) / (r - 1).

Sum of 2 terms in an harmonic sequence = 2ab / (a + b).

Sum of n terms in an arithmetic sequence, S n = (n/2).

cos (A - B) = cos A cos B + sin A sin B.

cos (A + B) = cos A cos B - sin A sin B.

sin (A - B) = sin A cos B - cos A sin B.

sin (A + B) = sin A cos B + cos A sin B.

tan θ = 1 / cot θ (OR) cot θ = 1 / tan θ.

cos θ = 1 / sec θ (OR) sec θ = 1 / cos θ.

sin θ = 1 / cose cθ (OR) cosec θ = 1 / si nθ.

Pythagoras Theorem: Hypotenuse 2 = Perpendicular 2 + Base 2.

Some of the important precalculus formulas are given below:

They also help in simplifying simple as well as complicated problems in precalculus. Precalculus formulas are indirectly used in finding the derivatives and integrals of functions. Vectors are elements that exist in the vector space and represent a quantity having both direction and magnitude. The important topics that fall under matrices are as follows: The subtopics that are covered under this are mentioned below.Ī matrix is a rectangular array where data is organized in the form of rows and columns. Under conic sections, students are introduced to different geometrical figures and their properties that will be used in calculus. The important topics covered are listed below. The precalculus functions topics are given below:Īrithmetic, harmonic and geometric sequences are the three types of sequences that fall under a precalculus course. The precalculus trigonometry topics covered are as follows:įunctions are binary relations between two sets where every element of the domain is mapped to exactly one element of the codomain. Trigonometry relates the sides of a right-angled triangle to its angles using trigonometric ratios. The list of polynomial topics that fall under precalculus are given below:

Modulus and Argument of Complex NumbersĪ polynomial is an algebraic expression that consists of variables, coefficients, and constants that are joined using algebraic operations like addition, multiplication, positive exponentiation, etc.

The topics covered under this course of precalculus are as follows. Such a number is of the form x + iy, where iy is the imaginary number. The various topics covered under precalculus are as follows:Ī complex number can be defined as a number that contains a real part and an imaginary part. Precalculus helps in preparing for higher-grade and college-level calculus courses.

Trig cheat sheet