Lesson 11: EXPONENTIAL
AND LOGARITHMIC
FUNCTIONS
Math 12
Plane and Spherical Trigonometry
OBJECTIVES
At the end of the lesson the students are expected to:
Define Exponential and Logarithmic Functions.
Graph Exponential and Logarithmic Functions.
Apply th
Lesson 4: GRAPHS OF
TRIGONOMETRIC FUNCTIONS
Math 12
Plane and Spherical Trigonometry
OBJECTIVES
At the end of the lesson the students are expected to:
Develop the properties of trigonometric functions.
Find the amplitude, period, phase shift and vertica
EXPONENTIAL AND
LOGARITHMIC
FUNCTIONS
EXPONENTIAL FUNCTION
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 t
PLANE AND SPHERICAL
TRIGONOMETRY
TRIGONOMETRY
Derived from the Greek words trigonon which means triangle
and metron which means to measure.
Branch of mathematics which deals with measurement of
triangles (i.e., their sides and angles), or more specificall
LESSON 2
TRIGONOMETRY OF RIGHT
TRIANGLES
THE SIX TRIGONOMETRIC FUNCTIONS
hypotenuse
Adjacent
side
Opposite
side
hypotenuse
Adjacent
side
Opposite
side
Let be an acute angle of a right triangle. The values of the six
trigonometric functions of are
length o
LESSON 3
TRIGONOMETRIC
FUNCTIONS OF ANGLES
COORDINATE PLANE
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
y
follows:
Quadrant
Lesson 2: TRIGONOMETRY
OF RIGHT TRIANGLES
Math 12
Plane and Spherical Trigonometry
OBJECTIVES
At the end of the lesson the students are expected to:
Define the six trigonometric functions as ratios of the
sides of a right triangle
Evaluate the trigonometr
Lesson 1
Trigonometric Functions
SPECIFIC OBJECTIVES:
At the end of the lesson, the student is expected to :
Define trigonometry.
Measure angles in rotations, in degrees and in radians.
Find the measures of coterminal angles.
Change from degree measur
Trigonometry
55
Lesson 10
Exponential and Logarithmic
Functions
SPECIFIC OBJECTIVES:
At the end of the lesson, the student should be able to :
Define exponential and logarithmic functions
Establish the relationship between exponential and logarithmic
fu
50
Trigonometry
Lesson 9
Oblique Triangles
SPECIFIC OBJECTIVES:
At the end of the lesson, the student is expected to:
Apply the Law of Sines to solve oblique triangles
Case 2: Two sides
and the
opposite
of the
sidestriangles.
are given
Apply
theangle
La
48
Trigonometry
Lesson 8
Trigonometric Equations
SPECIFIC OBJECTIVES:
At the end of the lesson, the student is expected to:
Define conditional equations.
Find exact solutions to trigonometric equations.
8.1 Trigonometric Equations
Definition 8.1
Trigono
29
Trigonometry
Lesson 5
Graphs of Trigonometric
Functions
SPECIFIC OBJECTIVES:
At the end of the lesson, the student is expected to:
Identify the amplitude, period, phase shift and vertical shift of a
sine or cosine function.
Sketch the graph of sine a
Lesson 2: TRIGONOMETRY OF
RIGHT TRIANGLES
Math 12
Plane and Spherical Trigonometry
OBJECTIVES
At the end of the lesson the students are expected to:
Define the six trigonometric functions as ratios of the sides of
a right triangle
Evaluate the trigonome
Lesson 6: TRIGONOMETRIC
IDENTITIES
Math 12
Plane and Spherical Trigonometry
OBJECTIVES
At the end of the lesson the students are expected to:
Review basic identities.
Simplify a trigonometric expression using identities.
Verify a trigonometric identity
Lesson 3: SOLUTIONS OF RIGHT
TRIANGLES
Math 12
Plane and Spherical Trigonometry
OBJECTIVES
At the end of the lesson the students are expected to:
Solve right triangles
Solve real-world problems using trigonometry
SOLUTION OF RIGHT TRIANGLE
To solve a ri
Lesson 4: TRIGONOMETRIC
FUNCTIONS OF ANGLES
Math 12
Plane and Spherical Trigonometry
OBJECTIVES
At the end of the lesson the students are expected to:
Define trigonometric functions in the Cartesian plane
Evaluate the trigonometric functions of the quad
Lesson 4: GRAPHS OF
TRIGONOMETRIC FUNCTIONS
Math 12
Plane and Spherical Trigonometry
OBJECTIVES
At the end of the lesson the students are expected to:
Develop the properties of trigonometric functions.
Find the amplitude, period, phase shift and vertica
TRIGONOMETRY
Math 12
Plane and Spherical Trigonometry
TRIGONOMETRY
Derived from the Greek words trigonon which means
triangle and metron which means to measure.
Branch of mathematics which deals with measurement of
triangles (i.e., their sides and angle