Introduction to Trigonometric
Functions
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• Trig functions are the
relationships amongst
various sides in right
triangles.
• You know by the
Pythagorean theorem
that the sum of the
squares of each of
the smaller sides
equals the square of
the hypotenuse, a 2  b2  c 2
A
c
b
C
a
You know in the above triangle that
B
a b  c
2
2
Trig functions are how the relationships
amongst the lengths of the sides of a
right triangle vary as the other angles
are changed.
2
How does this relate to trig?
A
sin(θ) = b/c
cos(θ) = a/c
tan(θ)= b/a
c
b
C
a
θ
B
Remember SOHCAHTOA
• Sine: Opposite/
Hypotenuse
• Cosine: Adjacent/
Hypotenuse
• Tangent: Opposite/
Adjacent
Practice!?
•
•
•
•
c=?
sin(θ)=
cos(θ)=
tan(θ)=
A
c
3
C
4
θ
B
Practice!?
•
•
•
•
b=?
sin(θ)=
cos(θ)=
tan(θ)=
θ
15
9
b
New Trig!
opp
• sin(θ)=
hyp
hyp
• csc(θ)=
opp
adj
• cos(θ)=
hyp
hyp
• sec(θ)=
adj
opp
• tan(θ)=
adj
adj
• cot(θ)=
opp
More Practice!
θ
• sin(θ)=
9
• cos(θ)=
• tan(θ)=
15
12
csc(θ)=
sec(θ)=
cot(θ)=
More Practice!
• sin(θ)=
9
θ
• cos(θ)=
• tan(θ)=
15
12
csc(θ)=
sec(θ)=
cot(θ)=
Time for a worksheet!