March 06, 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.
March 06, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
March 06, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
March 06, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
Simplify the following trigonometric expressions.
1.
cot x tan x
March 06, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
2.
sin2 θ + tan2 θ + cos2 θ
sec θ
March 06, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
3.
1 - cos2 θ
sin θ
March 06, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
4.
sec(-x) cos(-x)
March 06, 2015
5.
1 + tan θ
1 + cot θ
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
March 06, 2015
March 06, 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
March 06, 2015
7.
1
1 - sin x
+
1
1 + sin x
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
March 06, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
Day 2: Solve for all x in the interval [0, 2 )
1.
sin2x - 2sinx + 1 = 0
March 06, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
2. 2 cos2x = 1
March 06, 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.
3. √2 tan x cos x - tan x = 0
March 06, 2015
Obj: To learn the basic trigonometric identities to solve
trigonometric expressions and equations.
HW:
(Reg) Day 1: Worksheet (5.1) finish
(Reg) (5.1) Pg. 411: 39, 41, 51, 53, 55, 57