February 09, 2010
5.1
Fundamental Identities
identity: statement that is true for all values of the
variable for which both sides of the equation are defined.
domain of validity: the set of all such values for which
both sides of the equation are defined.
February 09, 2010
Refer to identities on Page 445
February 09, 2010
Pythagorean Identities:
cos2θ + sin2θ = 1
1 + tan2θ = sec2θ
cot2θ + 1 = csc2θ
February 09, 2010
2. If tan (π/2 - θ) = -5.32, find cot θ.
February 09, 2010
Simplify the following expressions.
3.
cot x tan x
February 09, 2010
4. 1 - cos2θ
sin θ
February 09, 2010
5.
sin2θ + tan2θ + cos2θ
sec θ
February 09, 2010
6.
sec(-x) cos(-x)
February 09, 2010
7.
1 + tan θ
1 + cot θ
February 09, 2010
8.
(sec x - tan x)(sec x + tan x)
sec x
February 09, 2010
9.
1
1 - sin x
+
1
1 + sin x
February 09, 2010
10.
1
sin2x
+
2
sec x
tan2x
February 09, 2010
Day 2
11.
1 - 2sinx + sin2x
February 09, 2010
Rewrite as a single trig. function.
12.
tan2x - 1
1 + tan x
February 09, 2010
Find all solutions to the equation in the interval [0, 2π)
without a calculator.
14. √2 tan x cos x - tan x = 0
February 09, 2010
15. 2 sin2x = 1