Trig Functions Of Acute Angles Worksheet Page 2
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16Cofunctions: Notice that
sin A = cos B
and that
cos A = sin B
These relations will always be true for the acute angles of a right triangle
tan A = cot B
and
sec A = csc B.
sin and cos are cofunctions
Since A and B are complementary then A + B = 90
tan and cot are cofunctions
and B = 90 - A, which gives us the cofunction
sec and cot are cofunctions
identities. *these are true for
ACUTE
angles
Cofunction Identities
sin A = cos (90 - A)
sec A = csc (90 - A)
tan A = cot (90 - A)
cos A = sin (90 - A)
csc A = sec (90 - A)
cot A = tan (90 - A)
The easiest way to look at this is that the angles of the cofunctions add up to 90 and are
therefore complementary.
For ex: Sin A = Cos B
sin 30⁰ = cos 60⁰
sec 40⁰ = csc 50⁰
so A + B = 90
tan 20⁰ = cot 70⁰
cos (2x + 3)⁰ = sin (3x
8)⁰
To solve this you would make
2x + 3 + 3x
8 = 90
Ex2: Writing Functions in Terms of Cofunctions
Write each term in terms of its cofunction.
1)
cos 52˚
2) tan 71˚
3) sec 24˚
4)
sin 9˚
5) cot 76˚
6) csc 45˚
Ex3: Solving Equations Using Cofunction Identities
Find one solution for each equation. Assume all angles are acute angles.
1)
cos (θ + 4)⁰ = sin (3θ + 2)⁰
2) tan (2θ
18)⁰ = cot (θ + 18)⁰
Classroom Ex3:
1)
cot (θ
8)⁰ = tan ( 4θ + 13)⁰
2) sec (5θ + 14)⁰ = csc (2θ
8)⁰
Chapter 2 Page 2
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