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trigonometry Group 2 TrigonoMatrix 9-Neutron

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Page 1: Trigonometry

trigonometry

Group 2

TrigonoMatrix

9-Neutron

Page 2: Trigonometry

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

What is Trigonometry?

Page 3: Trigonometry

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

Page 4: Trigonometry

• 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

Page 5: 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

Page 6: Trigonometry

Function and Relation

Page 7: Trigonometry

• 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?

Page 8: Trigonometry

Examples:

Page 9: Trigonometry

• 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?

Page 10: Trigonometry

Examples:

Page 11: Trigonometry

Trigonometric Functions

Page 12: Trigonometry

SINE

COSINE

TANGENT

SINE, COSINE, TANGENT

Page 13: Trigonometry

• Greek Letter Theta) represents the unknown angle degree.

Page 14: Trigonometry

Op

po

site

Hypot

enus

eAdjacent

Page 15: Trigonometry

• 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”

Page 16: Trigonometry

• 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

Page 17: Trigonometry

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

Page 18: Trigonometry

Find the values of the three trigonometric functions of

.

Page 19: Trigonometry

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

Page 20: Trigonometry

• 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

Page 21: Trigonometry
Page 22: Trigonometry