Trigonometry

Hipparcus – 190 BC to 120 BC – born in Nicaea (now Turkey) was a Greek astronomer who is considered to be one of the first to use trigonometry.

Arjit SaraswatSubmitted by :-

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Parts of a Right Triangle

Hypotenuse

A

B

CNow, imagine that you move from angle A to angle B still facing into the triangle.

Imagine that you, the happy face, are standing at angle A facing into the triangle.

The hypotenuse is neither opposite nor adjacent.

You would be facing the perpendicular side

and standing next to the base.

You would be facing the perpendicular side

and standing next to the base.

Perpendicular

Base

AryabhattaIndian Mathematician

ReviewHypotenuse

Hypotenuse

Perpendicular

BaseA

B

For Angle A

This is the Perpendicular

This is the Base

For Angle B

AThis is the Base

This is the Perpendicular

Perpendicular

Base

B

PythagorusSamian Mathematician

Trig Ratios

We can use the lengths of the sides of a right triangle to form ratios. There are 6 different ratios that we can make.

Using Angle A to name the sidesUse Angle B to name the sides

The ratios are still the same as before!!

A

BHypotenuse

Base

Perpendicular

)(

)(

)(

)(

)(

)(

BaseB

larPerpendicuP

HypotenuseH

BaseB

HypotenuseH

larPerpendicuP

)(

)(

)(

)(

)(

)(

larPerpendicuP

BaseB

BaseB

HypotenuseH

larPerpendicuP

HypotenuseH

RamanujamIndian Mathematician

Trig Ratios

• Each of the 6 ratios has a name• The names also refer to an angle

Hypotenuse

Base

PerpendicularA

Sine of Angle A = H

P

Cosine of Angle A = H

B

Tangent of Angle A =B

P

Cosecant of Angle A = P

H

Secant of Angle A = B

H

Cotangent of Angle A = P

B

EuclidGreek Mathematician

Trig RatiosHypotenuse

Base

PerpendicularIf the angle changes from A to B

The way the ratios are made is the same

B

Sine of Angle = H

P

Cosine of Angle = H

B

Tangent of Angle =B

P

Cosecant of Angle = P

H

Secant of Angle = B

H

Cotangent of Angle = P

B

B

B B

B

B B

FreitagGerman Mathematician

Trig Ratios

• Sine, Cosine and Tangent ratios are the most common. Base

PerpendicularA

Hypotenuse• Each of these ratios has an abbreviation

Sin A =

Cos A =

Tan A =

Cosec A=

Sec A =

Cot A =

Sine of Angle A = H

P

Cosine of Angle A = H

B

Tangent of Angle A =B

P

Cosecant of Angle A = P

H

Secant of Angle A = B

H

Cotangent of Angle A = P

B

John DeeEnglish Mathematician

SPHCBHTPB

BaseA

B

PerpendicularHypotenuse

Here is a way to remember how to make the 3 basic Trig Ratios

1) Identify the Perpendicular side and Base for the appropriate angle

2) Remember “SPHCBHTPB” and it means :-

Some People Have Curly Beautiful Hair To Preserve Beauty

Use the underlined letters to make the word SPH-CBH-TPB

QueteletFlemish Mathematician

6 10

8A

BFirst we will find the Sine, Cosine andTangent ratios for Angle A.

Next we will find the Sine, Cosine, andTangent ratios for Angle B Base

Perpendicular

Remember SPH-CBH-TPB

4

3

8

6

5

4

10

8

5

3

10

6

B

P

H

B

H

PSin A =

Cos A =

Tan A =

Cosec B =

Sec B =

Cot B = 3

4

6

8

5

3

10

6

5

4

10

8

P

B

B

H

P

H

LameFrench Mathematician

Example

AlbertiItalian Mathematician

Trigonometric ratios

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Trigonometry

Trigonometry

Arjit Saraswat

Class : X B

School : GMSSS-35,Chd

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