February 11, 2015
(5.1) Fundamental Trigonometric Identities
Objective: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
Why: Trigonometric Identities are used in various functions in
calculus.
February 11, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
February 11, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
February 11, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
Simplify the following trigonometric expressions.
1.
cot x tan x
February 11, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
2.
sin2 θ + tan2 θ + cos2 θ
sec θ
February 11, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
3.
1 - cos2 θ
sin θ
February 11, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
4.
sec(-x) cos(-x)
February 11, 2015
5.
1 + tan θ
1 + cot θ
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
February 11, 2015
6.
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
(sec x - tan x)(sec x + tan x)
sec x
February 11, 2015
7.
1
1 - sin x
+
1
1 + sin x
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
February 11, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
8.
1
sin2x
+
sec2x
tan2x
February 11, 2015
Day 2: Factor.
1.
1 - 2sinx + sin2x
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
February 11, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
Rewrite as a single trig. function.
2.
tan2x - 1
tan x + 1
February 11, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
Find all solutions to the equation in the interval [0, 2π)
without a calculator.
13. √2 tan x cos x - tan x = 0
February 11, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
14. 2 sin2x = 1
February 11, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
Six Functions in One Picture
ϴ
F
A
G
ϴ
B
E
C
D
February 11, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
HW:
(HR)
(5.1) Pg. 410: 9-17odd, 21-31odd