Assignment #2
Name: _Mera Yousef_
Chapter 4
Exponential Functions are functions that
can be written in the form of f(x) = a^x,
where a is a positive constant and x is
the variable. These functions have a
characteristic shape of a curve that is
always increasing or decreasing,
depending on whether the base a is
greater than or less than 1. For example,
the function f(x) = 2^x is an exponential
function with base 2, and its graph looks
like an upward sloping curve. Similarly,
the function g(x) = (1/2)^x is an
exponential function with base 1/2, and
its graph is a downward sloping curve.
Exponential Function (II) refers to a more
general form of an exponential function
that includes a constant multiplier and a
constant exponent. It can be written as
f(x) = ab^x, where a and b are positive
constants, and x is the variable. For
example, the function f(x) = 2(3/4)^x is
an exponential function of the form f(x)
= ab^x, where a = 2 and b = 3/4.
Exponential Growth and Decay are
phenomena that can be modeled by
exponential functions. Exponential
growth occurs when a quantity increases
at a constant rate proportional to its
Chapter 5
Trig Functions, or trigonometric functions, are
mathematical functions that relate the angles of a right
triangle to the ratios of the lengths of its sides. The three
primary trigonometric functions are sine, cosine, and
tangent. They are usually denoted by the symbols sin θ, cos
θ, and tan θ, respectively. For example, if θ is an angle in a
right triangle with adjacent side a and hypotenuse h, then
sin θ = a/h, cos θ = h/a, and tan θ = a/h.
Inverse Trig Functions are functions that reverse the effect
of the primary trigonometric functions. They are used to
find the angle given the ratio of two sides in a right triangle.
The three primary inverse trigonometric functions are
inverse sine, inverse cosine, and inverse tangent, usually
denoted by the symbols sin^(-1), cos^(-1), and tan^(-1),
respectively.
Right Triangles are triangles with one angle measuring 90
degrees, called the right angle. They have special properties
that allow for the use of trigonometric functions to find the
lengths of their sides and angles. In a right triangle, the side
opposite the right angle is called the hypotenuse, while the
other two sides are called the adjacent and opposite sides.
Trig Functions of Any Angle are the extension of the
primary trigonometric functions to any angle, not just
angles in right triangles. They are defined using the unit
circle, where an angle in standard position is measured as
the arc length on the unit circle.
The Periodic Function is a function that repeats its values
after a certain interval, called the period. The sine and
Chapter 6
Fundamental Identities are a set of
equations that relate the values of the
trigonometric functions. These identities
are true for all values of the variables, and
they are used to simplify trigonometric
expressions and solve trigonometric
equations. The six fundamental
trigonometric identities are:
1. sin^2 θ + cos^2 θ = 1
2. 1 + tan^2 θ = sec^2 θ
3. 1 + cot^2 θ = csc^2 θ
4. sin(-θ) = -sin θ
5. cos(-θ) = cos θ
6. tan(-θ) = -tan θ
For example, if we are given the
expression cos^2 θ - sin^2 θ, we can use
the first fundamental identity to simplify it
as:
cos^2 θ - sin^2 θ = cos^2 θ - (1 - cos^2 θ) =
2cos^2 θ - 1
Trig Equations are equations that involve
trigonometric functions and are solved for
the values of the variables. These
equations can be linear, quadratic, or
higher-order equations, and they are
solved using various methods, including
factoring, completing the square, and
using the quadratic formula. Some
