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Algebra 2
Tuesday, April 07, 2009
Section 12.2: Trigonometric Functions of Acute Angles
e
s
nu
p
hy
te
n
o
opposite side
θ
adjacent side
Trigonometric Functions:
opposite
sin θ = hypontenuse
csc θ =
cos θ =
adjacent
hypontenuse
sec θ =
tan θ =
opposite
sin θ
=
adjacent
cos θ
cot θ =
hypontenuse
opposite
hypontenuse
adjacent
adjacent = cos θ
opposite
sin θ
1
Algebra 2
Tuesday, April 07, 2009
Section 12.2: Trigonometric Functions of Acute Angles
Example: An acute angle is in standard position and
its terminal side passes through ( 2 , 4 ). Find the
values of the six trigonometric functions.
sin θ =
csc θ =
cos θ =
sec θ =
tan θ =
cot θ =
2
Algebra 2
Tuesday, April 07, 2009
Section 12.2: Trigonometric Functions of Acute Angles
Pythagorean Identity:
sin2 θ + cos2 θ = 1
Numerical Proof: Type this into your calc...
sin230° + cos230° = ???
sin2320° + cos2320° = ???
Cofunction Identities:
(think of complementary angles)
sin ( 90° - θ ) = cos θ
csc ( 90° - θ ) = sec θ
cos ( 90° - θ ) = sin θ
sec ( 90° - θ ) = csc θ
tan ( 90° - θ ) = cot θ
cot ( 90° - θ ) = tan θ
Numerical Proof: Type this into your calc...
sin (30°) =
cos (90° - 30°) =
3
Algebra 2
Tuesday, April 07, 2009
Section 12.2: Trigonometric Functions of Acute Angles
Example: Find the measure of acute angle θ, if
cot θ = tan 20°
4
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