9.5 Trigonometric Ratios

Sin-Cos-Tan

What is Trigonometry?

• Trigonometry (from Greek trigōnon "triangle" + metron "measure") is a branch of mathematics that studies triangles and the ratios between their sides and the angles between these sides. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies. It is also the foundation of the practical art of surveying.

http://en.wikipedia.org/wiki/Trigonometry

Right Angle Trigonometry

The Ratio used in Right Angle Trigonometry are

Sine – Sin

Cosine – Cos

Tangent - Tan a

b

c

Right Angle Trigonometry

The Ratio used in Right Angle Trigonometry

a

b

c

b

aATan

c

bACos

c

aASin

Right Angle Trigonometry

The Ratio used in Right Angle Trigonometry

a

b

c

adjacent

oppositeTanA

hypotenuse

adjacentCosA

hypotenuse

oppositeSinA

Right Angle Trigonometry

The Ratio used in Right Angle Trigonometry

a

b

c

TOAadjacent

oppositeTanA

CAHhypotenuse

adjacentCosA

SOHhypotenuse

oppositeSinA

How to Remember the Ratio

Chief SOH – CAH - TOA

TOAadjacent

oppositeTanA

CAHhypotenuse

adjacentCosA

SOHhypotenuse

oppositeSinA

Right Angle Trigonometry

The Ratio used in Right Angle Trigonometry

4167.12

5

9231.13

12

3846.13

5

ATan

ACos

ASin

A

B

C

5

12

13

Right Angle Trigonometry

The Ratio used in Right Angle Trigonometry

4167.6

5.2

9231.5.6

6

3846.5.6

5.2

ATan

ACos

ASin

A

B

C

5

12

13

65.25.6