MAPA INSTITUTE OF TECHNOLOGY
Department of Mathematics
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If x and b are real numbers such that b > 0 and
b 1, then f(x) = bx is an exponential function
with base b.
Examples of exponential functions:
a) y = 3x
b) f(x) = 6x
c) y = 2x
Example: Evaluate th
DERIVATION OF LAW OF SINES
Let ABC be an oblique triangle with sides a, b,
and c opposite their respective angles as shown
in the figure below. If an altitude h is drawn to the
base, we can write the following relationship:
DEFINITION: TRIGONOMETRIC EQUATIONS
Equations that involve the trigonometric
functions are called trigonometric equations.
Solving a trigonometric equation means the
same thing as solving an algebraic equation, like
finding the val
DEFINITION: If f is a one-to-one function with
domain A and range B, then its inverse f 1 is
the function with domain B and range A defined
f 1 x y f y x
For a function to have an inverse, it must be
one-to-one. Since th
DEFINITION OF TERMS:
Spherical Trigonometry is a branch of trigonometry
that concerns with triangles extracted from the surface
of the sphere.
Great Circle is a circle obtained by passing a section
through the center of the sphere
SOLUTION OF RIGHT TRIANGLE
Solving a triangle means determining the measures of
all sides and angles of the triangles. In solving problems
involving right triangle, the following steps may be
Sketch the required tr
DEFINITION: A trigonometric identity is an
equation involving the trigonometric functions
that holds for all values of the variable.
BASIC TRIGONOMETRIC IDENTITIES
GRAPH OF SINE FUNCTION:
(y = sin x)
Properties of Sine Function Graph:
1. The graph crosses the x-axis at the initial point,
endpoint and midpoint of a cycle. These points
are called the zeros of the function.
2. A maximu
The coordinate axes divide the plane into four parts
called quadrants. For any given angle in standard
position, the measurement boundaries for each
quadrant are summarized as follows:
Quadrant II 0
Derived from two Greek words:
trigonon which means triangle and
metron which means to measure.
A branch of mathematics which deals
with the measurement of triangles:
three sides and three angles.
CLASSIFICATION OF TRIANGLES
Consider a right triangle with as one of its acute angles. The
trigonometric ratios are defined as follows .