October 31, 2014
October 31, 2014
Questions
October 31, 2014
Pythagorean, Reciprocal, and Quotient Properties
The Reciprocal Properties
sec•x =
1
cos•x
1
sin•x
csc•x =
1
cot•x =
tan•x
The Quotient Properties
tan•x =
sin•x
cos•x
=
sec•x
csc•x
cot•x =
cos•x
sin•x
=
csc•x
sec•x
The Three Pythagorean Properties
cos2x + sin2x = 1
1 + tan2x = sec2x
cot2x + 1 = csc2x
1. Using the triangle at the right, prove the Pythagorean Property.
sin2x + cos2x = 1
a
c
b
2. Show how the reciprocal property tan•x = sin•x/cos•x can
be transformed to express tan•x in terms of sec•x and csc•x.
3. By appropriate operations on the Pythagorean property:
cos2x + sin2x = 1, derive the Pythagorean property:
1 + tan2x = sec2x.
October 31, 2014
Assignment: p. 161 (Q1-Q8, 1-9 odd)