trigonometry

trigonometry

Group 2

TrigonoMatrix

9-Neutron

• Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. 

What is Trigonometry?

• Trigonometry is found all throughout geometry, as every straight-sided shape may be broken into as a collection of triangles. 

• It is necessary for the computation of the bell curve.

• Contributed to advances in the fields of acoustics, architecture, cartography, civil engineering, geophysics etc.

Importance of Trigonometry

• Modern applications of trigonometry include its use in satellite navigation, naval and aviation industries, the composition of music, and all types of digital imaging.

• It has also become critical in the construction of modern buildings.

Applications of Trigonometry

Function and Relation

• Function is a relation between set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

What is Function?

Examples:

• Relation is simply a set of ordered pairs.

• The first elements in the ordered pairs (the x values), form the domain.

• The second elements in the ordered pairs (the y values) form the range.

What is Relation?

Examples:

Trigonometric Functions

SINE

COSINE

TANGENT

SINE, COSINE, TANGENT

• Greek Letter Theta) represents the unknown angle degree.

Op

po

site

Hypot

enus

eAdjacent

• For you to easily remember the formulas, just remember the shortcut “Soh Cah Toa”

• Soh for Sin= opposite/Hypotenuse

• Cah for Cos= Adjacent/Hypotenuse

• Toa for Tan= Opposite/Adjacent

“Soh Cah Toa”

• The hypotenuse is the longest side and is always opposite the right angle.

• The opposite and adjacent sides refer to another angle, other than the 90o.

Right Triangle Trigonometry

A

A

Finding Sin, Cos and TanExample:

8

10

6

10

8

10

6

6

8

CosAdj

Hyp

Adj

OppTan

4

5

3

5

4

3

Hyp

OppSin

Find the values of the three trigonometric functions of

.

4

3

? Pythagorean Theorem:(3)² + (4)² = c²

5 = c

opp

hyp 4

5

adj

hyp

3

5 opp

adj

4

3

sin cos tan

5

• A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree?

Example:

50

71.5°

?

tan 71.5°

tan 71.5° 50

y

y = 50 (tan 71.5°)

y = 50 (2.98868)

149.4y ft

Opp

Hyp