Name______________________________
Cofunctions
Date____________
10H Per_________
Given right triangle ABC, where C is a right angle,
a) What is the relationship between A and B ?
Express each as a fraction:
b) sinA =
The letters “CO” tell everything:
cosB =
- sine and COsine are COfunctions
c) tanA =
- secant and COsecant are COfunctions
cotB =
- tangent and COtangent are COfunctions
d) secA =
- COfunctions of COmplimentary
(add to 90o) angles are equal.
cscB =
This leads us to three pairs of cofunctions:
1.
2.
3.
Ex. 1: Find the value of θ for which sin(θ) = cos(15o) is true.
Ex. 2: Solve for θ: sec(θ) = csc (θ + 60)
Ex. 3: Solve for θ: cot(θ + 10) = tan(3θ + 8)
Ex. 4: Express each function as the cofunction of a positive acute angle that is less than 45o:
a) tan(75o)
b) sin(100o)
c) cos(265o)
d) csc(305o)
Practice:
1. For what value of x does tan(x + 10) = cot (40 + x)?
2. If sin 6 A  cos 9 A , then what is mA ?
3. If x is a positive acute angle and sec x  csc( x  20 o ) , find the value of x.
4. Express each function as the function value of an acute angle that is less than 45o:
a) tan(94o)
b) sec(245o)
c) sin(281o)
5. Find the exact value of csc(240o)
6. If cot  
5
37
and csc  0 , find sec in simplest radical form.