www.iTutoring.com -­‐ NOTES Complementary Angle Theorem Name _________________________________ Date ___________________ Period _______ ! and " are complementary angles
sin ! =
cos ! =
a
c
csc ! =
b
c
sec ! =
a
tan ! =
b
c
a
c
b
b
cot ! =
a
sin " =
b
c
csc " =
c
b
cos " =
a
c
sec " =
c
a
tan " =
b
a
cot " =
a
b
"
c
a
!
b
Cofunctions of complementary angles are equal
Trigonometric Cofunctions
sine and cosine
tangent and cotangent
cosecant and secant
Given ! and " are complementary angles...
sin ! = cos "
tan ! = cot "
csc ! = sec "
cos ! = sin "
cot ! = tan "
sec ! = csc "
Examples
complementary
complementary
complementary
sin 50° = cos 40°
tan 32° = cot 58°
csc 85° = sec 5°
cofunctions
cofunctions
cofunctions
complementary
sin
π
π
= cos
6
3
cofunctions
complementary
tan
complementary
π
π
= cot
4
4
csc
cofunctions
π
π
= sec
3
6
cofunctions
Use the Complementary Angle Theorem to simplify the following expressions
sin 25° – cos 65°
tan 12°
cot 78°
1 + sin2 33° + sin2 57°
cot 82° –
sin 8°
sin 82°
© iTutoring.com
Complementary Angle Theorem Pg. 2 Cofunctions of complementary angles are equal
Given ! and " are complementary angles...
sin ! = cos "
tan ! = cot "
csc ! = sec "
cos ! = sin "
cot ! = tan "
sec ! = csc "
© iTutoring.com
Complementary Angle Theorem Pg. 3