trigonometry
DESCRIPTION
project in trigoTRANSCRIPT
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