Who am I?
I was credited for preparing
tables of sines used for solving problems in
astronomy and a Greek mathematician of
antiquity introduced trigonometry as a
systematized body of knowledge.
“I am the eight letter of the alphabet +
the symbol of the imaginary number +
double the first letter of polynomial +
(3a-2a) +r + c + the inverse of “n”
+ 20th letter-1”
YES, I am
Hipparcus
of Bithynia
(190-120 B.C.)
Welcome to the world of
mathematics
Area of specialization
Trigonometry
Now you know the person behind trigonometry
let us now explore his works.
One common mnemonic is to remember the
SOH-CAH-TOA.
In this lesson, we will consider the
sine, cosine and tangent functions and
the meaning of the two angle namely:
the angle of elevation and depression
respectively.
Let us consider this right triangle.
What have you observed?
The side opposite the right angle is the hypotenuse.
The sides opposite the two acute angles are legs
called opposite and adjacent of angle .
t
But our problem here is to
solve for the unknown angle or
the theta “θ”. Now we can apply
the mnemonic that we have,
the famous SOH-CAH-TOA.
The sine of an angle is the ratio
of the opposite side to the
hypotenuse side.
SOH
opposite
hypotenuse
Example:
Calculate the value of sin θ in the
following triangle.
Solution:
The cosine of an angle is the
ratio of the adjacent side and
hypotenuse side.
CAH
adjacent
hypotenuse
Example:
Calculate the value of cos θ in the
following triangle.
Solution:
The tangent of an angle is the
ratio of the opposite side and
adjacent side.
TOA
opposite
adjacent
Example:
Calculate the value of tan θ in the
following triangle.
Solution:
Application
Find the values of the three trigonometric functions
(soh, cah, toa) for each of the following indicated angles.
P
a.)
M
21
20
29
b.)
53
t
45
Activity 2
The two angles
Angle of Elevation
The word “elevation” means “rise” or “move up”.
Angle of elevation is the angle between the
horizontal and the line of sight to an object
above the horizontal.
Angle of Depression
The word “depression” means “fall” or “drop”.
Angle of depression is the angle between the
horizontal and the line of sight to an object
beneath the horizontal.
Take a look at the example below.
In the picture below, an observer is standing at the
top of a building and looking straight ahead at the
birds (horizontal line). The observer must raise his
eyes to see the airplane (slanting line). The angle
formed between the two lines is called the angle
of elevation.
Take a look at the example below.
In the picture below, an observer is standing at the
top of a building and looking straight ahead at the
birds (horizontal line). The observer must lower
his eyes to see the car parked (slanting line). The
angle formed between the two lines is called the
angle of depression.
Assignment
Find the height of a hot air balloon which is
directly above a nipa hut if the angle of
depression of a carabao, 62 m away from the
nipa hut is 14 º55’.
Note: Use the possible trigonometric function/s in
answering your assignment.
Study your lessons.
Don’t give up!
I know you can do it.