Search for notes by fellow students, in your own course and all over the country.
Browse our notes for titles which look like what you need, you can preview any of the notes via a sample of the contents. After you're happy these are the notes you're after simply pop them into your shopping cart.
Title: Trigonometry Basic
Description: If You are start learning trigonometry then you want to learn its basics rules and formulas.in this notes you will learn its basics.
Description: If You are start learning trigonometry then you want to learn its basics rules and formulas.in this notes you will learn its basics.
Document Preview
Extracts from the notes are below, to see the PDF you'll receive please use the links above
Introduction To Trigonometry
Trigonometric Ratios
Opposite & Adjacent Sides in a Right Angled Triangle
In the ΔABC right-angled at B, BC is the side opposite to ∠A, AC is the hypotenuse and AB
is the side adjacent to ∠A
...
Consider a line segment OP joining
a point P on the circle to the centre which makes an angle θ with the x-axis
...
sinθ =
PQ
OP
=
OQ
cosθ =
tanθ =
OP
PQ
OQ
cosecθ =
secθ =
cotθ =
=
PQ
OP
OQ
PQ
= PQ
1
OQ
=
OP
OQ
PQ
=
=
= OQ
1
sinθ
cosθ
=
1
PQ
1
OQ
cosθ
sinθ
Visualisation of Trigonometric Ratios Using a Unit Circle
Relation between Trigonometric Ratios
1
cosecθ =
secθ =
tanθ =
cotθ =
sinθ
1
cosθ
sinθ
cosθ
cosθ
sinθ
=
1
tanθ
Trigonometric Ratios of Specific Angles
Range of Trigonometric Ratios from 0 to 90 degrees
For 0
∘
∘
≤ θ ≤ 90 ,
0 ≤ sinθ ≤ 1
0 ≤ cosθ ≤ 1
0 ≤ tanθ < ∞
1 ≤ secθ < ∞
0 ≤ cotθ < ∞
1 ≤ cosecθ < ∞
and secθ are not defined at 90
cotθ and cosecθ are not defined at 0
∘
tanθ
∘
...
Variation of trigonometric ratios from 0 to 90 degrees
As θ increases from 0 to 90
∘
∘
sinθ
increases from 0 to 1
...
tanθ
increases from 0 to ∞
...
cosecθ
secθ
increases from 1 to ∞
...
Standard values of Trigonometric ratios
∘
∠A
0
sin A
0
cos A
1
tan A
0
cosec A
N ot def ined
sec A
cot A
1
N ot def ined
30
∘
45
∘
∘
60
1
1
√3
2
√2
2
√3
1
1
2
√2
2
1
√3
1
√3
2
2
√3
√3
√2
√2
1
2
√3
2
1
√3
∘
90
1
0
N ot def ined
1
N ot def ined
0
Trigonometric Ratios of Complementary Angles
Complementary Trigonometric ratios
If θ is an acute angle, its complementary angle is 90
for trigonometric ratios of complementary angles
...
The following relations hold true
∘
sec(90
− θ) = cosecθ
Trigonometric Identities
Trigonometric Identities
2
2
sin θ + cos θ = 1
2
2
1 + cot θ = coesc θ
2
2
1 + tan θ = sec θ
Title: Trigonometry Basic
Description: If You are start learning trigonometry then you want to learn its basics rules and formulas.in this notes you will learn its basics.
Description: If You are start learning trigonometry then you want to learn its basics rules and formulas.in this notes you will learn its basics.