Download θ θ

PreCalculus Class Notes TEI2 Simplifying and Factoring Trigonometric Expressions
Many of the algebraic skills that you have already learned can be used to simplify trigonometric
functions.
1. Multiplying binomials
(1 − x)(1 − x)
2. Adding two expressions
y
x
y
x
+
(1 − cosθ )(1 − cosθ )
tan t + cot t
3. Factoring an expression
Difference of squares
x2 − 1
sec2 θ − 1
x2 + x
sin 2 x + sin x
x2 + 2x + 1
tan 2 θ + 2 tan θ + 1
Common Factor
Trinomials
Simplify the trigonometric expression completely.
1
cos 2 θ
−
sin θ sin θ
1 − cos 2 θ
1 + cosθ
Multiply out first
If you convert to sin/cos first, you get
csc 2 θ sec 2 θ . Is it equivalent?
(cot θ + tan θ ) 2
csc 2 θ + sec 2 θ = csc 2 θ sec 2 θ
sin 2 θ cscθ
sin 2 t (1 + cot 2 t )
Factor the trigonometric expression and simplify, if possible.
sin 2 t − cos 2 t
cosθ sin 2 θ + cos3 θ
sin 4 t − cos 4 t
tan 2 x + 4 tan x − 12
csc x cot 2 x + 6 csc x cot x − 27 csc x
2 sin 2 x + 3sin x − 2