Answer these Questions: Type of the triangle in fig 1 What’s the side opposite to right angle Called? Which property relate the sides of right triangle? fig1 P H B
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Answer these Questions:Type of the triangle in fig 1What’s the side opposite to right angle Called?
Which property relate the sides of right triangle?
fig1
P H
B
What Is Trigonometry?The word “Trigonometry” is derived from
Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning measure).
It is used to find Distances and Heights of objects in real life.
A trigonometric ratio is a ratio of the lengths of two sides in a right triangle.
TRIGONOMETRIC RATIO
Three basic trigonometric ratios: sine cosine tangent each of which is the ratio of one side to
another..
How to Use TrigonometryTake the right-angled
triangle ABC. Notice that A and C
are acute angles and B is right angle.
Acute angles are taken under consideration for finding
T-ratios.
A
B C
Hypotenuse
Base
Perpendicular
First, Label the Sides Let’s take angle A
under consideration.
Each side is given a label in relation to angle ‘A’. There is the hypotenuse, perpendicular and base side.
A
B C
Hypotenuse
Base
Perpendicular
So, Now the TrigonometryAs previously
mentioned, the trigonometric functions: sine, cosine and tangent are ratios of the sides in relation to angle ‘A’.
A
B C
Hypotenuse
Base
Perpendicular
Firstly, Sinesine is shortened to
“sin”.
Possible values of sine A are between 0 and 1.
hyp
perSinA
A
B C
Hypotenuse
Base
Perpendicular
Now Cosine cosine is shortened to
“cos”.
As with sine A, possible values of cosine A are between 0 and 1.
A
B C
Hypotenuse
Base
Perpendicular
hyp
baseAcos
And Finally Tangent tangent is
shortened to “tan”.
Any value for tangent A is possible, both positive and negative.
base
perAtan
A
B C
Hypotenuse
Base
Perpendicular
opposite
adjacent
hyp
baseAcos
Hyp
perAsin
base
perTanA
A
B C
Hypotenuse
Base
Perpendicular
S C T
P B P
H H B
Sin P H Cos B H Tan P B
6
8
10
4
5
3
5
4
3
10
8
10
6
6
8
A B
C
H
PSinA
H
BCosA
B
PTanA
(P)
(B)
(H)
Identify perpendicular , hypotenuse and base in relation to angle C in given fig.
A
B C
Other Trigonometric-ratiosCosecant In short it is cosec.Secant In short it is sec.Cotangent In short it is cot.
P
H
AecA
sin
1cos
P
B
AA
tan
1cot
B
H
AA
cos
1sec
Example 1: Finding the Value of Trigonometric Ratio
sin A, cos A,tan A,cosec A,sec A and cot A.
A
BC
17
15
8
sin A, cos A,tan A,cosec A,sec A and cot A.
A
BC
17
15
8
Sin A
Cos A
Tan A
17
15
H
P
17
8
H
B
8
15
B
P
solution
15
17
sin
1cos
P
H
AecA
8
17
cos
1sec
B
H
AA
A
BC
17
15
8
15
8
tan
1cot
P
B
AA
Find the values of all the trigonometric ratios of .
4
3
? Pythagoras Theorem:(3)² + (4)² = c²
5 = c
5
5
3cos
P
B3
4tan
B
P
4
5
sin
1cos
ec
3
5
cos
1sec
5
4sin
H
P
5
3
tan
1cot
Example 2:If tan A=4/3 then calculate sinA.cosASOLUTION
A
B C
Let us first draw a right ABCAs we know
3k
4k
Therefore BC=4k,AB=3k, where k is any positive number.
Now,by using Pythagoras theorem we have AC2 = AB2 + BC2
=(3K)2 +(4K)2
=9K2 + 16K2
AC2 =25K2
AC=5K
3
4
AB
BC
B
PTanA
25
12
5
3
5
4cos.sin AA
A
B C4k
3k5K
5
4
5
4sin
k
k
AC
BC
B
PA
5
3
5
3cos
k
k
AC
AB
H
BA
Answer= 12/25
COMMON ERRORALERT
Students tend to make simple mistakes bymislabeling the perpendicular and base
To overcome this mistake first determine theHypotenuse.
The side opposite to acute angle under Consideration is the perpendicular.
A
C B
2524
7
Find each trigonometric ratio. 1.Sin B 2.Cos B 3.Tan B 4. cosec B 5. sec B 6. cot B
QUESTION 1
In ABC right angle at B, if
calculate all other trigonometric ratios.
QUESTION 2
12
13sec A